Variational methods are a strong tool in proving existence of solutions of differential equations. In this paper we prove a strong form of the mountain pass theorem which was prompted by the need of a theorem which, besides an existence statement for critical points, gives in addition information about the “fine structure” of the functional near to them. The abstract theorems are based on results in [H1,H2,H3] and [EH1,EH2]. Related results have been also obtained in [PS1,PS2].