We investigate the effect of mass accretion onto massive main sequence
stars on their internal structure and evolution. Adopted accretion ra
tes and accretion time scales are in the range applying to massive Cas
e B binary systems. For the first time, we incorporate the influence o
f molecular weight gradients on convection in this context. In contras
t to earlier studies, we find that the so called ''rejuvenation'' of t
he mass accreting star does not always take place. Rather, stellar mod
els with a chemical structure unlike that of single stars may be obtai
ned. We investigate which physical parameters determine whether rejuve
nation occurs, namely the fraction of the core hydrogen burning time s
pent until the onset of accretion, the amount of matter accreted, the
initial mass of the accreting star, and the efficiency of convection i
n regions of stabilizing mean molecular weight gradients. Further an,
the evolution of accretion stars until central carbon ignition is inve
stigated. We find that the main result of non-rejuvenation is a much s
maller helium core mass and accordingly longer core helium burning tim
es compared to single stars. This may lead to blue supergiant position
s adjacent to the main sequence band in the HR diagram, and to blue su
pergiant pre-supernova configurations. Possible relations to the obser
ved distribution of luminous stars in the HR diagram of the LMC and to
the progenitor df supernova 1987 A are discussed.