∂x

of an asymptote of capillary-gravity waves on the interface of two fluids of finite depth B.Loginov, E.Trofimov ∗ N.Kochin by the methods of complex variable solved the two dimensional problem about a motion of two non-mixed incompressible fluids with densities %1 and %2. In the problem the layers of the fluids are bounded by horizontal planes. The boundary between the fluids has a period λ and moves with a constant horizontal velocity without changing its form. In this work we use the methods of the bifurcation theory of solutions of nonlinear equations with group symmetry [2,3] to solve the similar three-dimensional problem in which the fluids have a surface tension. The potential flows of the fluids, that bifurcate from the flow with a constant velocity V along the x-axis, are described by the system ∆Φ1 = 0, −1 < z < f(x, y); ∆Φ2 = 0, f(x, y) < z < k; ∂Φ1 ∂z = 0, z = −1; ∂Φ