  Despite 50 years of extensive binary research we have to conclude that the
Roche lobe overflow/mass transfer process that governs close binary evolution
is still poorly understood. It is the scope of the present paper to lift a tip
of the veil by studying the spin-up and spin-down processes of the O-type
components of WR+O binaries. We critically analyze the available observational
data of rotation speeds of the O-type components in WR+O binaries. By combining
a binary evolutionary code and a formalism that describes the effects of tides
in massive stars with an envelope in radiative equilibrium, we compute the
corresponding rotational velocities during the Roche lobe overflow of the
progenitor binaries. In all the studied WR+O binaries, we find that the O-type
stars were affected by accretion of matter during the RLOF of the progenitor.
This means that common envelope evolution which excludes any accretion onto the
secondary O-star, has not played an important role to explain the WR+O
binaries. Moreover, although it is very likely that the O-type star progenitors
were spun-up by the mass transfer, many ended the RLOF/mass transfer phase with
a rotational velocity that is significantly smaller than the critical rotation
speed. This may indicate that during the mass transfer phase there is a
spin-down process which is of the same order as, although significantly less
than that of the spin-up process. We propose a Spruit-Tayler type dynamo
spin-down suggested in the past to explain the rotation speeds of the mass
gainers in long-period Algols.
