  Applying the time-dependent Ginzburg-Landau equations, transitions between
metastable states of a superconducting ring are investigated in the presence of
an external magnetic field. It is shown that if the ring exhibits several
metastable states at a particular magnetic field, the transition from one
metastable state to another one is governed by both the relaxation time of the
absolute value of the order parameter tau_{|psi|} and the relaxation time of
the phase of the order parameter tau_{phi}. We found that the larger the ratio
tau_{|psi|}tau_{phi} the closer the final state will be to the absolute minimum
of the free energy, i.e. the thermodynamic equilibrium. The transition to the
final state occurs through a subsequent set of single phase slips at a
particular point along the ring.
