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An asymptotic approach for a Schroedinger type equation with non selfadjointHamiltonian of a special type in the case of two close degeneracy (turning)points is developed. Both real and complex degeneracy points are treated by amethod of matched asymptotic expansions in the context of a unifying approach.An asymptotic expansion near degeneracy point containing the parabolic cylinderfunctions is constructed and the transition matrix connecting the coefficientsof adiabatic modes in front of and behind the degeneracy point is derived.  A simple non-technical recipe is also provided, which enables one to applyresults to different physical problems without performing intermediatecalculations.

A unifying asymptotic approach for nonadiabatic transitions near pairs of real or complex turning points