  The aim of this paper is to establish the uniform convergence of the
densities of a sequence of random variables, which are functionals of an
underlying Gaussian process, to a normal density. Precise estimates for the
uniform distance are derived by using the techniques of Malliavin calculus,
combined with Stein's method for normal approximation. We need to assume some
non-degeneracy conditions. First, the study is focused on random variables in a
fixed Wiener chaos, and later, the results are extended to the uniform
convergence of the derivatives of the densities and to the case of random
vectors in some fixed chaos, which are uniformly non-degenerate in the sense of
Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for
random variables in the second Wiener chaos, and an application to the
convergence of densities of the least square estimator for the drift parameter
in Ornstein-Uhlenbeck processes is discussed.
