  About a quarter of massive binary stars undergo mass transfer while both
stars burn hydrogen at their cores, first on the thermal and then on the
nuclear timescale. The nuclear timescale mass transfer leads to observable
counterparts: the semi-detached so-called massive Algol binaries. However,
comprehensive model predictions for these systems are sparse. We study them
using a large grid of ~10,000 detailed binary evolution models calculated with
the stellar evolution code MESA, covering initial donor masses between 10-40
M$_{\odot}$ and initial orbital periods above 1.4 d, at a metallicity suitable
for the Large Magellanic Cloud (LMC). Our models imply ~30, or ~3% of the
~1,000 core hydrogen burning O-star binaries in the LMC to be currently in the
semi-detached phase. Our donor models are up to 25-times more luminous than
single stars of identical mass and effective temperature, which agrees with the
observed Algols. A comparison of our models with the observed orbital periods
and mass ratios implies rather conservative mass transfer in some systems,
while very inefficient one in others. This is generally well reproduced by our
spin-dependent mass transfer algorithm, except for the lowest considered
masses. The observations reflect the slow increase of the surface nitrogen
enrichment of the donors during the semi-detached phase all the way to CNO
equilibrium. We also investigate the properties of our models after core
hydrogen depletion of the donor star, when these models correspond to
Wolf-Rayet/helium+OB star binaries. A dedicated spectroscopic survey of massive
Algol systems may allow to derive the dependence of the efficiency of thermal
timescale mass transfer on the binary parameters, as well as the efficiency of
semiconvective mixing in the stellar interior. This would be a crucial step
towards reliable binary models up to the formation of supernovae and compact
objects.
