A method of fundamental solutions has been used to study adiabatic transition amplitudes in two energy level systems for a class of Hamiltonians allowing some simplifications of Stokes graphs corresponding to such transitions. It has been shown that for simplest such cases the amplitudes take the Nikitin-Umanskii form but for more complicated ones they are formed by a sum of terms strictly related to a structure of Stokes graph corresponding to such cases. These results are in a full agreement with the ones of Joye, Mileti and Pfister [Phys. Rev.  A44, 4280 (1991)] found by other method.

PACS numbers: 03.65.-w, 03.65.Sq, 02.30.Lt, 02.30.Mv