Ballistic charge transport through mesoscopic superconductor-norma met
al-superconductor (SNS) microbridges is investigated on the basis of t
he Keldysh technique. At low voltages we find a peak in the conductanc
e which is caused by multiple Andreev reflection of quasiparticles tra
pped in the pair potential well of the N-layer in the presence of inel
astic relaxation there. For larger voltages inelastic relaxation in th
e N-layer plays no role, quasiparticles are accelerated out of the N-l
ayer and relax in superconducting banks. We demonstrate that even at e
V T << Delta the system has a finite subgap conductance, i.e. dissipat
ive current can flow through a superconducting constriction both with
and without normal metal inclusion. In this case dissipation arises fr
om pairbreaking due to acceleration of virtually created subgap quasip
articles by the electric field. In the voltage range V similar to Delt
a/e we analyze the temperature dependence of the subharmonic gap struc
ture which turns out to be most pronounced at T similar to Delta and v
anishes at T --> 0 and T --> T-c. This behavior is the result of a cou
nter current induced by thermally excited quasiparticles.