Josephson and quasiparticle currents in SNcNS contacts are calculated
for the regimes of ballistic constriction ''c''. The relation between
the current and electronic densities of states in NS proximity bilayer
is found. The effect of the proximity N laver on the Andreev and norm
al reflections of electrons at the constriction is studied. Excess cur
rent at large voltages and subharmonic structure at low bias are analy
zed as a function of material parameters of N and S and transparency o
f the NS interface. The appearance of new series of subharmonic peaks
due to two-gap structure in the density of states of proximity NS elec
trodes is demonstrated. The relation between excess and critical curre
nts is analyzed. The model is relevant for SNS junctions of constricte
d geometry which is realized in S-2DEG-S and step-edge high T-c SNS co
ntacts.