  The proof by Ullmo and Zhang of Bogomolov's conjecture about points of small
height in abelian varieties made a crucial use of an equidistribution property
for ``small points'' in the associated complex abelian variety.
  We study the analogous equidistribution property at $p$-adic places. Our
results can be conveniently stated within the framework of the analytic spaces
defined by Berkovich. The first one is valid in any dimension but is restricted
to ``algebraic metrics'', the second one is valid for curves, but allows for
more general metrics, in particular to the normalized heights with respect to
dynamical systems.
