This poster presented results from the Large Magellanic Cloud Near-Infrared Synoptic Survey (LMCNISS) for classical and Type II Cepheid variables that were identified in the Optical Gravitational Lensing Experiment (OGLE-III) catalogue. Multi-wavelength time-series data for classical Cepheid variables are used to study light-curve structures as a function of period and wavelength. We exploited a sample of ∼1400 classical and ∼80 Type II Cepheid variables to derive Period–Wesenheit relations that combine both optical and near-infrared data. The new Period–Luminosity and Wesenheit relations were used to estimate distances to several Local-Group galaxies (using classical Cepheids) and to Galactic globular clusters (using Type II Cepheids). By appealing to a statistical framework, we found that fundamental-mode classical Cepheid Period–Luminosity relations are non-linear around 10–18 days at optical and near-IR wavelengths. We also suggested that a non-linear relation provides a better constraint on the Cepheid Period–Luminosity relation in Type Ia Supernovæ host galaxies, though it has a negligible effect on the systematic uncertainties affecting the local measurement of the Hubble constant.