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[Abridged] We test the evolutionary model of cool close binaries on theobserved properties of near contact binaries (NCBs). Those with a more massivecomponent filling the Roche lobe are SD1 binaries whereas in SD2 binaries theRoche lobe filling component is less massive. Our evolutionary model assumesthat, following the Roche lobe overflow by the more massive component (donor),mass transfer occurs until mass ratio reversal. A binary in an initial phase ofmass transfer, before mass equalization, is identified with SD1 binary. We showthat the transferred mass forms an equatorial bulge around the less massivecomponent (accretor). Its presence slows down the mass transfer rate to thevalue determined by the thermal time scale of the accretor, once the bulgesticks out above the Roche lobe. It means, that in a binary with a (typical)mass ratio of 0.5 the SD1 phase lasts at least 10 times longer than resultingfrom the standard evolutionary computations neglecting this effect. This is whywe observe so many SD1 binaries. Our explanation is in contradiction topredictions identifying the SD1 phase with a broken contact phase of theThermal Relaxation Oscillations model. The continued mass transfer, past massequalization, results in mass ratio reversed. SD2 binaries are identified withthis phase. Our model predicts that the time scales of SD1 and SD2 phases arecomparable to one another. Analysis of the observations of 22 SD1 binaries, 27SD2 binaries and 110 contact binaries (CBs) shows that relative number of bothtypes of NCBs favors similar time scales of both phases of mass transfer. Totalmasses, orbital angular momenta and orbital periods of SD1 and SD2 binaries areindistinguishable from each other whereas they differ substantially from thecorresponding parameters of CBs. We conclude that the results of the analysisfully support the model presented in this paper.

Evolution of Cool Close Binaries -- Rapid Mass Transfer and Near Contact Binaries