  We consider the spin angular momentum evolution of the accreting components
of Algol-type binary stars. In wider Algols the accretion is through a disc so
that the accreted material can transfer enough angular momentum to the gainer
that material at its equator should be spinning at break-up. We demonstrate
that even a small amount of mass transfer, much less than required to produce
today's mass ratios, transfers enough angular momentum to spin the gainer up to
this critical rotation velocity. However the accretors in these systems have
spins typically between 10 and $40\,$per cent of the critical rate. So some
mechanism for angular momentum loss from the gainers is required. We consider
generation of magnetic fields in the radiative atmospheres in a differentially
rotating star and the possibility of angular momentum loss driven by strong
stellar winds in the intermediate mass stars, such as the primaries of the
Algols. Differential rotation, induced by the accretion itself, may produce
such winds which carry away enough angular momentum to reduce their rotational
velocities to the today's observed values. We apply this model to two systems
with initial periods of 5\,d, one with initial masses 5 and $3\,\rm{M}_{\odot}$
and the other with 3.2 and $2\,\rm{M}_{\odot}$. Our calculations show that, if
the mass outflow rate in the stellar wind is about $10\,$per cent of the
accretion rate and the dipole magnetic field is stronger than about $1\,$kG,
the spin rate of the gainer is reduced to below break-up velocity even in the
fast phase of mass transfer. Larger mass loss is needed for smaller magnetic
fields. The slow rotation of the gainers in the classical Algol systems is
explained by a balance between the spin-up by mass accretion and spin-down by a
stellar wind linked to a magnetic field.
