  We study electron propagation in a molecular lattice model. Each molecular
site involves doubly degenerate electronic states coupled to doubly degenerate
molecular vibration, leading to a so--called E-e type of Jahn-Teller
Hamiltonian. For weak electron-phonon coupling and in the anti-adiabatic limit
we find that the orbital degeneracy induces an intersite pairing mechanism
which is absent in the standard non-degenerate polaronic model. In this limit
we analyse the model in the presence of an additional on-site repulsion and we
determine, within BCS mean field theory, the region of stability of
superconductivity. In one dimension, where powerful analytical techniques are
available, we are able to calculate the phase diagram of the model both for
weak and for strong electron-phonon coupling.
