abstract: The ''General Problem of the Stability of Motions'' deals with the evolution of initial states in unbounded time domains. From the very beginning two different (but complementary) classes of problems were studied. From one side, with Lagrange, begun the research of criteria for the stability of equilibria of general systems of Mechanics. On the other side, with Laplace, started the study of the stability of the ''Système du Monde''. In both these fields studies developed rapidly giving rise to the ''qualitative analysis'' of nonlinear systems. My talk will be devoted to focus some selected arguments and to follow their history till present days.