  We treat the problem of self-consistently interacting bosons in the presence
of a finite (but macroscopic) potential well within a quasi-classical
approximation for the normal component and the order parameter. We solve the
equilibrium problem and show, that actually condensation occurs in two steps.
One already at low densities with Bose condensation only in the well and
another one corresponding to the usual condensation in bulk. The peak and width
of the distribution of trapped particles in the well display a distinct
signature of the local condensation. A possible connection to recent
experiments with excitons is discussed.
