  A novel method is developed for constructing periodic solutions of a model
equation describing nonlocal Josephson electrodynamics. This method consists of
reducing the equation to a system of linear ordinary differential equations
through a sequence of nonlinear transformations. The periodic solutions are
then obtained by a standard procedure which are represented in terms of
trigonometric functions. It is found that the large time asymptotic of the
solution exhibits a steady profile which does not depend on initial conditions.
