A set of 27 evolutionary models of cool close binaries was computed under the assumption that their evolution is influenced by the magnetized winds. Initial periods of 1.5, 2.0 and 2.5 d were considered. For each period three values of 1.3, 1.1 and 0.9 solar mass were taken as the initial masses of the more massive components. Here the results of the computations of the first evolutionary phase are presented, which starts from the initial conditions and ends when the more massive component reaches its critical Roche lobe. In all considered cases this phase lasts for several Gyr. For binaries with the higher total mass and/or longer initial periods this time is equal to, or longer than the main sequence life time of the more massive component. For the remaining binaries it amounts to a substantial fraction of this life time. From the statistical analysis of models, the predicted period distribution of detached binaries with periods shorter than 2 d was obtained and compared to the observed distribution from the ASAS data. An excellent agreement was obtained under the assumption that the period distribution in this range is determined solely by the mass and angular momentum loss due to the magnetized winds. This result indicates, in particular, that virtually all cool detached binaries with periods of a few tenths of a day, believed to be the immediate progenitors of W UMa-type stars, were formed from detached systems with periods around 2-3 d and that magnetic braking is the dominant formation mechanism of cool contact binaries. It operates on the time scale of several Gyr rendering them rather old, with age of 6-10 Gyr. The results of the present analysis will be used as input data to investigate the subsequent evolution of the binaries, through the mass exchange phase and contact or semi-detached configuration till the ultimate merging of the components.
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