  We examine the conditions needed to accomplish stimulated Raman adiabatic
passage (STIRAP) when the three levels (g, e and f) are degenerate, with
arbitrary couplings contributing to the pump-pulse interaction (g - e) and to
the Stokes-pulse interaction (e-f). We show that in general a sufficient
condition for complete population removal from the g set of degenerate states
for arbitrary, pure or mixed, initial state is that the degeneracies should not
decrease along the sequence g, e and f. We show that when this condition holds
it is possible to achieve the degenerate counterpart of conventional STIRAP,
whereby adiabatic passage produces complete population transfer. Indeed, the
system is equivalent to a set of independent three-state systems, in each of
which a STIRAP procedure can be implemented. We describe a scheme of unitary
transformations that produces this result. We also examine the cases when this
degeneracy constraint does not hold, and show what can be accomplished in those
cases. For example, for angular momentum states when the degeneracy of the g
and f levels is less than that of the e level we show how a special choice for
the pulse polarizations and phases can produce complete removal of population
from the g set. Our scheme can be a powerful tool for coherent control in
degenerate systems, because of its robustness when selective addressing of the
states is not required or impossible. We illustrate the analysis with several
analytically solvable examples, in which the degeneracies originate from
angular momentum orientation, as expressed by magnetic sublevels.
