  We study the dynamics of a dilute spherical model with two body interactions
and random exchanges. We analyze the Langevin equations and we introduce a
functional variational method to study generic dilute disordered models. A
crossover temperature replaces the dynamic transition of the fully-connected
limit. There are two asymptotic regimes, one determined by the central band of
the spectral density of the interactions and a slower one determined by
localized configurations on sites with high connectivity. We confront the
behavior of this model to the one of real glasses.
