We have performed experiments in a superconductor-normal-metal-superconduct
or single-electron transistor in which then is an extra superconducting str
ip partially overlapping the normal-metal island in good metal-to-metal con
tact. The superconducting proximity effect gives rise to current peaks at v
oltages below the quasiparticle threshold. We interpret these peaks in term
s of the Josephson-quasiparticle process and discuss their connection with
the proximity-induced energy gap in the normal-metal island.