Abstract: We define $n$ numbers that, for maps that are not necessarily differentiable, play the role of the values of the Lyapunov exponent . We then show that for a large family of repellers and of hyperbolic sets of differentiable maps, the values of the new exponent coincide with the classical ones. We also discuss the relation of the new Lyapunov exponents with the dimension theory of dynamical systems for invariant sets of continuous maps. Namely, we use the new exponents to establish an upper bound for the Hausdorff dimension of a class of invariant measures supported on nonconformal invariant sets for maps that are not necessarily differentiable.