On some methods for investigating stability

This article contains various algorithms for investigating the stability (using the apparatus of the splitting method) of certain classes of non-autonomous systems of linear and quasi-linear ordinary differential equations. The results complement previously known results. Each of the algorithms presented can be regarded (in a certain sense) as a development of the classical method of normal forms, which is very effective in the study of non-linear systems for analysing linear and quasilinear non-autonomous systems of ordinary differential equations.