We discuss difficulties in explaining the distribution of AGB stars in the 25–12 vs. 12–K color–color diagram by steady-state radiatively driven models, and propose that the discrepancy may be due to changes of mass-loss rate with the time scales of ∼ 100 yr.

Analysis of the 1993–4 eclipse in the slow symbiotic nova PU Vul (4900-d binary orbital period) and 1995-9 photoelectric observations in V and R bandpasses show that the cool component of this object is pulsating AGB variable with a 215-d pulsation period. Basic properties of the components of the system are discussed.

Results of regular observations of about 20 Miras and semiregular variables (∘ Cet, R Leo, R Aql, U Her, χ Cyg, R Tri, and others) in 1994–1999 are presented. The monitoring includes optical spectroscopy, optical (UBV) and infrared (JHKLM) photometry, high-resolution radio spectroscopy in the 1.35-cm water-vapour maser line (on the 22-m radio telescope in Pushchino). Optical spectroscopy shows that the appearance of strong Balmer emission lines in Miras may be a rare event, and the presumed shock waves are thus weak. The H2O maser flux generally correlates with visual light curves of the stars with some delay Δφ = 0.1 – 0.4P (P is the variability period). For R Leo, R Cas, and U Aur strong flares in the Hφ line, observed in 1997–1998, were followed by corresponding outbursts of the H2O maser emission about 2P later. This sequence of events is probably caused by a shock wave propagating outward in the stellar atmosphere and consecutively initiating the Hα emission and, later, the maser flare at a larger distance from the stellar surface.

Based on the statistical parallaxes, the mean absolute magnitudes and the spatial kinematical parameters were determined as functions of the periods for Mira variables given in the GCVS-4 and selected stars for which new kinematical data were obtained during the last decade. The BC were derived for the oxygen-rich Miras and the P–L relation was compared with predictions from pulsation theory. The following findings result from this analysis:

1) With respect to Miras, the GCVS-4 is complete down to V = 9m.

2) The kinematical and orbital parameters indicate a higher age for the oxygen-rich Miras pulsating with smaller periods.

3) The Mbol-period relation of the oxygen-rich Miras shows a low dispersion and does not depend on the pulsation mode. The resulting P–L relation is a superposition of P–L relations of different pulsation modes.

4) The fraction of the fundamental mode pulsators decreases with increasing pulsation period.

Variations of light curve parameters in Mira variables with progressive period changes have been studied. They lead to a consistent sequence of the stars which is related to the helium flash model.

Cyclic period variations (P ≈ 19400d) in T Cep were investigated. As the result of cross-correlation analysis, relations between individual cycle parameters were found. Relations between period–amplitude, hump–amplitude, hump–minimum magnitude, and others have been obtained.

The Hipparcos survey team discovered thousands of new variables, including M giants with periods as short as a day, which appear to have maintained rough phase coherence over a period of more than three years. New optical and infrared photometry has been obtained as part of an effort to understand the nature of these anomalous stars.

Some pulsating post-AGB stars have been observed with an Automatic Photometry Telescope (APT) and a considerable amount of precise photometric data has been accumulated for these stars. The datasets, however, are still sparse, and this is a problem for applying nonlinear time series: for instance, modeling of attractors by the artificial neural networks (NN) to the datasets. We propose the optimization of data interpolations with the genetic algorithm (GA) and the hybrid system combined with NN. We apply this system to the Mackey–Glass equation, and attempt an analysis of the photometric data of post-AGB variables.

Using observations obtained in the pilot campaign of the EROS-2 microlensing survey we observed 290 Cepheids towards the LMC and 590 Cepheids towards the SMC. We present the constraints they give to stellar pulsation theory. We detect a statistically significant break in the slope of the period–luminosity relation for SMC fundamental mode Cepheids with periods shorter than 2 d and discuss its origin.

We apply the Barnes–Evans variant of the Baade–Wesselink method to Cepheids in the LMC and SMC in an attempt to determine the distance directly to individual stars in these galaxies and to determine the metallicity effect on the Cepheid period–luminosity relation. We now have K-band light curves for a sample of SMC stars as well as for many Cepheids in young clusters in the LMC. Using the FV, (V – K) calibration of Fouqué & Gieren (1997) we find preliminary evidence for a metallicity effect which makes metal poor Cepheids brighter. This is at odds with earlier results based on optical photometry and the reason is not entirely understood yet.

We present linear radii for four Cepheid variable stars, spanning a pulsation period range from 3 to 11 d, measured with the Navy Prototype Optical Interferometer (NPOI). We compare these radii to those found using traditional indirect methods, and to various period–radius relations found in the literature.

A summary of the first results of a search for Cepheids in IC 1613 is reported along with a short discussion of the adopted technique, a comparison of the characteristics of Cepheid light curves in the Galaxy, Magellanic Clouds and IC 1613, and a possible application for a P–L relation derivation. First overtone Cepheids have been identified for the first time in a galaxy farther than the Magellanic Clouds.

We present preliminary results from a synoptic photometric variability survey of the galactic globular cluster M3. These data consist of between 9 and 13 nights of data, the sampling allows a minimum detectable period of 10 minutes and is complete to MV ~ 21.

Of the several types of variable stars that occur in globular clusters, RR Lyrae stars have deservedly received the most attention. These stars are ideally suited for comparisons between evolution and pulsation theory, they play a prominent role in distance determinations, and are valuable tracers of the oldest stellar populations. After a brief discussion of technical aspects, we review some of the recent observational work.

The Large Magellanic Cloud (LMC) is widely considered a corner-stone of the astronomical distance scale. However, a difference of 0.2−0.3 mag exists in its distance as predicted by the short and long distance scales. Distances to the LMC from Population II objects are founded on the RR Lyrae variables. We have undertaken an observational campaign devoted to the definition of the average apparent luminosity, and to the study of the mass–metallicity relation for RR Lyrae stars in the bar of the LMC. These are compared with analogous quantities for cluster RR Lyrae stars. The purpose is to see whether an intrinsic difference in luminosity, possibly due to a difference in mass, might exist between field and cluster RR Lyrae stars, which could be responsible for the well-known dichotomy between short and long distance scales. Preliminary results are presented on the V and B − V light curves, the average apparent visual magnitude, and the pulsational properties of 102 RR Lyrae stars in the bar of the LMC, observed at ESO in January 1999. The photometric data are accurately tied to the Johnson photometric system. Comparison is presented with the photometry of RR Lyrae stars in the bar of the LMC obtained by the MACHO collaboration (Alcock et al. 1996). Our sample includes 9 double-mode RR Lyrae stars selected from Alcock et al. (1997) for which an estimate of the metal abundance from the ΔS method is presented.

We have applied the Baade–Wesselink method to two field RR Lyrae stars, i.e. SW And and RR Cet, and derived their distances and physical parameters. With respect to previous B–W analyses we have applied the following improvements: i) use of all sets of available data, after proper comparison for homogeneity and compatibility; ii) use of the most recent and accurate model atmospheres, with turbulent velocity Vturb = 4 km s−1 and the no-overshooting approximation, and comparison with other treatments of convection; iii) use of the instantaneous gravity along the pulsation cycle rather than the mean value; iv) comparison with modified radial velocity curves according to various assumptions on radial velocity gradients in the atmosphere; and v) careful reanalysis of the temperature scale. The main aim of this study is to evaluate the effect of the above items on the B–W results and verify whether any (or a combination) of them can possibly account for the discrepancy of the absolute magnitude zero-point with respect to other independent determinations.

The two nearby galaxies, M31 and M33, are stepping stones for most of our current efforts to understand the evolving universe at large scales. We are undertaking a long term project, called DIRECT, to improve the direct distance estimate to M31 and M33. The massive photometry we have obtained as part of our project over the past 3 years provides us with very good light curves for known and new Cepheid variables, a large number of eclipsing binaries and other variable stars.

Pulsating variables stars have had a long and prominent history in helping to map out the local Universe. Current observational techniques now make it possible to identify examples of all non-degenerate radial pulsating variables throughout much of the Local Group. I review our current knowledge of such variables in the dwarf galaxies of the Local Group. This summary tries to highlight some recent results that help underscore the use of these stars as important tools to study the physical nature of their parent galaxies as well as their continued use as important distance indicators of nearby galaxies.

Based on consistent stellar evolution and pulsation calculations for Cepheids, we analyse the effect of metallicity on period–luminosity relationships. We discuss the main uncertainties of the results inherent to stellar evolution calculations and linear stability analysis.

Baade–Wesselink radii derived using VJHK photometry are used to test the metallicity dependence of the Cepheid P–L relation using three collections of metallicity estimates from the literature. The hypothesis that Cepheids at the LMC metallicity ([Fe/H] ~ −0.2) could be several tenths of a magnitude fainter than at solar metallicity is not supported by the evidence.