  Many population synthesis and stellar evolution studies have addressed the
evolution of close binary systems in which the primary is a compact remnant and
the secondary is filling its Roche lobe, thus triggering mass transfer.
Although tidal locking is expected in such systems, most studies have neglected
the rotationally-induced mixing that may occur. Here we study the possible
effects of mixing in the mass-losing stars for a range in secondary star masses
and metallicities. We find that tidal locking can induce rotational mixing
prior to contact and thus affect the evolution of the secondary star if the
effects of the Spruit-Tayler dynamo are included both for angular momentum and
chemical transport. Once contact is made, the effect of mass transfer tends to
be more rapid than the evolutionary time scale, so the effects of mixing are no
longer directly important, but the mass transfer strips matter to inner layers
that may have been affected by the mixing. These effects are enhanced for
secondaries of 1-1.2 Msun and for lower metallicities. We discuss the possible
implications for the paucity of carbon in the secondaries of the cataclysmic
variable SS Cyg and the black hole candidate XTE J1118+480 and for the
progenitor evolution of Type Ia supernovae. We also address the issue of the
origin of blue straggler stars in globular and open clusters. We find that for
models that include rotation consistent with that observed for some blue
straggler stars, evolution is chemically homogeneous. This leads to tracks in
the HR diagram that are brighter and bluer than the non-rotating main-sequence
turn-off point. Rotational mixing could thus be one of the factors that
contribute to the formation of blue stragglers.
