  Let $P(M,G)$ be a principal fiber bundle and $E(M,N,G,P)$ be an associate
fiber bundle. Our interested is to study harmonic sections of the projection
$\pi_{E}$ of $E$ into $M$. Our first purpose is to give a stochastic
characterization of harmonic section from $M$ into $E$ and a geometric
characterization of harmonic sections with respect to its equivariant lift. The
second purpose is to show a version of Liouville theorem for harmonic sections
and to prove that section $M$ into $E$ is a harmonic section if and only if it
is parallel.
