Local solvability by quadratures over the field of meromorphic germs

As it is known, the solvability of linear differential equations in quadratures is defined by it's Galois group. Since it is difficult to find this group explicitely it is reasonable to investigate situations in which the solvability can be detected in terms of coefficients of the system.
I'll present a criteria of solvability in quadratures of linear systems in a neigbourhood of an irregular singular point. In the case when the system has one or two singulas points the criteria allows to investigate the global solvability over the field of rational functions. I'll consider some knowm examples (in particulat the Bessl equation) and suggest some open porblems.