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tokens: gainer has an initial mass of 2.7 M ⊙ . With CF = 0.95 one has a shell with an initial mass of 0.135 M ⊙ . The solidly rotating core keeps its mass of 2.565 M ⊙ during the entire evolution. At the end of RLOF A, the mass of the gainer has grown up to 6.936 M ⊙ . Since the core maintains its initial mass, the mass of the shell raises up to 4.371 M ⊙ , containing 63% of the gainer’s mass (CF = 0.37). At the end of RLOF B, the mass of the gainer is again somewhat larger and the value of CF shrinks to 0.31. Fig. 4. Mass fraction of the core (CF) decreases with time during the evolution of the system shown in Figs. 1 – 3 . This is not so different from the evolution of a shell with, for example, an initial value of CF = 0.5 that ultimately evolves into a massive shell with CF = 0.2 (80% of the mass of the gainer being in the shell), giving rise to magnetic fields and magnetic braking that are very similar to those obtained with an initial value of CF = 0.95. This value was used in all our calculations. 3.4. Calculated cases We found 44 binaries for which the equatorial velocity of the gainer was published. These systems are shown in Tables 1 and 2 . Table 1. Calculated equatorial velocities of gainers that best fit observations. Notes. Masses are in M ⊙ , orbital periods in days and v eq in km s −1 . The masses mentioned by the observations of Glazunova Yushcenko (2008) are from Budding et al. (2004) . Table 2. Calculated equatorial velocities of gainers fitting observations less good than in Table 1 . Notes. Masses in M ⊙ and orbital periods in days. Masses for V356 Sgr are from Dominis et al. (2005) . Masses in Glazunova Yushcenko (2008) are from Budding et al. (2004) and Brancewicz Dworak (1980) . For every binary in these tables, we calculated the evolution of a number of possible progenitors. In the case of conservative evolution, the initial orbital period P 0 of every progenitor was determined from the presently observed period P 1 with relation ( 13 ), which obeys to the rule of conservation of angular momentum: The subscript d is for the donor and g for the gainer. Although we calculated the orbital period with relations ( 10 )–( 12 ) using our code, relation ( 13 ) yields correct initial periods in the case of conservative evolution. This demonstrates that neglecting the spin angular momenta of the individual stars, as done in relation ( 13 ), is of minor importance. In the case of liberal evolution initial periods are determined with relation ( 14 ). This relation is valid when all matter that leaves the system takes only the orbital angular momentum of the involved stars. Here, M is the total mass of the system, so that: The quantity Δ M SW , the amount of mass that leaves the system as stellar wind, is always small compared to the stellar masses. The quantity Δ M OUT is the amount of RLOF mass that is not accreted by the gainer. This amount can be large and is difficult to predict. In our sample of 44 binaries, only two of them (V356