This communication summarizes the investigations of the relationship between the minimum binary period and the evolution of very short period hydrogen-rich cataclysmic binaries /CB's/.
In the first work /Paczyński, 1981/ some ideas were developed concerning an influence of gravitational radiation on the evolution of CB's, and some quantitative predictions
were done. In the next paper /Paczyński and Sienkiewicz, 1981, hereafter referred to as PS/ more detailed numerical calculations were performed. We considered a widely accepted picture
of such binaries. They are believed to have a white dwarf primary component surrounded with an accretion disk. The secondary component, probably the lower main sequence star or degenerate dwarf, overflows its Roche lobe, and matter flows from the inner Lagrangian point towards the disk. In all known cases but one, the binary orbits are circular. No hydrogen-rich CB's are observed with periods below 80 minutes. Because the nuclear evolution cannot be of any importance for the secondary, we assumed that angular momentum loss due to gravitational radiation is the driving force which causes the mass transfer and a cataclysmic activity.
We followed the evolution of such system with a very simple and fast code, and the best input physics actually available /PS, Sienkiewicz, 1981/. We have calculated a large number
of evolutionary tracks for many values of a total mass of a binary and the initial mass of the secondary.