  We revisit the adiabatic criterion in stimulated Raman adiabatic passage for
the three-level $\Lambda$-system, and compare the situation with and without
nonlinearity. In linear systems, the adiabatic condition is derived with the
help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a
procedure that breaks down in the presence of nonlinearity. Using an explicit
example relevant to photoassociation of atoms into diatomic molecules, we
demonstrate that the proper way to derive the adiabatic condition for the
nonlinear systems is through a linearization procedure.
