  In order to model the processes taking place in systems with Josephson
contacts, a differential equation on a torus with three parameters is used. One
of the parameters of the system can be considered small and the methods of the
fast--slow systems theory can be applied. The properties of the phase--lock
areas -- the subsets in the parameter space, in which the changing of a current
doesn't affect the voltage -- are important in practical applications. The
phase-lock areas coincide with the Arnold tongues of a Poincare map along the
period. A description of the limit properties of Arnold tongues is given. It is
shown that the parameter space is split into certain areas, where the tongues
have different geometrical structures due to fast--slow effects. An efficient
algorithm for the calculation of tongue borders is elaborated. The statement
concerning the asymptotic approximation of borders by Bessel functions is
proven.
