  To provide a solid analytic foundation for the module approach to conditional
risk measures, our purpose is to establish a complete random convex analysis
over random locally convex modules by simultaneously considering the two kinds
of topologies (namely the $(\varepsilon,\lambda)$--topology and the locally
$L^0$-- convex topology). This paper is focused on the part of separation and
Fenchel-Moreau duality in random locally convex modules. The key point of this
paper is to give the precise relation between random conjugate spaces of a
random locally convex module under the two kinds of topologies, which enables
us to not only give a thorough treatment of separation between a point and a
closed $L^{0}$-convex subset but also establish the complete Fenchel-Moreau
duality theorems in random locally convex modules under the two kinds of
topologies.
