  A microscopic model of the molecular magnet V15 is used to study mechanisms
for the adiabatic change of the magnetization in time-dependent magnetic
fields. Effects of the Dzyaloshinskii-Moriya interaction, the most plausible
source for the energy-level repulsions that lead to adiabatic changes of the
magnetization, are studied in detail. We find that the energy-level repulsions
that result from this interaction exhibit a strong dependence on the direction
of the applied field. We also discuss the role of magnetic anisotropy in the
molecule Mn12 -acetate.
