  We discuss some of the basic theoretical aspects of current-carrying states
in superconducting superlattices with tunnel barriers in the mesoscopic regime,
when the superconducting layer thickness is small compared to the BCS coherence
length but large compared to the atomic scale. We establish the necessary
conditions for the observation of the classical Josephson effect (with
sinusoidal current-phase dependence) and derive self-consistent analytical
expressions for the critical Josephson current. These expressions are
proportional to an additional small factor and have unusual temperature
dependence as compared with the single-junction case. For certain parameter
values, the superconducting gap exhibits an exponential decrease due to
pair-breaking effect of the supercurrent. The supercurrent can completely
destroy the superconductivity of the system above a certain characteristic
temperature (lower than the transition temperature of individual layers). In
this paper, we also study the effect of intrabarrier exchange interactions. We
show that this effect is strongly enhanced compared with the single- junction
case and can manifest itself in an exponential decrease of the critical
temperature.
