The mountain-pass lemma of Abrosetti and Rabinowitz gives conditions under which a smooth mapping \(F: X\to {\mathbb{R}}\), where X is a Banach space, has a critical point. The hypotheses are simply that F display mountain-pass structure relative to some points \(x_ 0\) and \(y_ 0\), and that the Palais-Smale compactness condition be verified. The critical value corresponding to the critical point in question is \[ c=\min_{g\in \Gamma}\max_{t\in [0,1]}F(g(t)), \] where \(\Gamma\) is the family of all continuous mappings g: [0,1]\(\to X\) obeying \(g(0)=x_ 0\), \(g(1)=y_ 0\). In this paper Ekeland's variational principle is used to extend the mountain-pass lemma in two directions. First, the author treats functions F which are only assumed to be locally Lipschitz. (A critical point for a locally Lipschitzian mapping \(F: X\to {\mathbb{R}}\) is one where 0 belongs to the Clarke generalized gradient of F.) Then he generalizes both the mountain-pass property and the minimax formula for the critical value to the set of continuous functions \(g: K\to X\), where K is any compact metric space. The proof is claimed to be new even in the original setting when F is smooth and \(K=[0,1]\).