On some methods for investigating stability

This article contains various algorithms for investigating the stability (u sing the apparatus of the splitting method) of certain classes of non-auton omous systems of linear and quasi-linear ordinary differential equations. T he results complement previously known results. Each of the algorithms pres ented can be regarded tin a certain sense) as a development of the classica l method of normal forms, which is very effective in the study of non-linea r systems for analysing linear and quasilinear non-autonomous systems of or dinary differential equations.