In this paper we consider the one-dimensional isothermal motion of two-phase mixture of viscous incompressible fluids in the absence of phase transitions. H.A. Rahmatulin’s scheme of force interaction and joint deformation phases is used for the stress tensor and vector interfacial phase. Pressure in phases differs by the amount of capillary jump. Reynolds numbers for each of the phases are assumed to be small. We used the expansion in the small parameter and deduced the system of first order equations corresponding to a zero approximation. The resulting system has a variable type. The conditions on the functional parameters of the equations for which the system has an elliptical form and is reduced to a system of Beltrami were formulated. The exact solution of a problem in an unbounded domain was obtained for the case of equal pressure phases and specially selected coefficients of the system. In general case, the numerical calculation of the problem was performed by the Runge-Kutta fourth-order accuracy. For the case of different pressures and small accelerations of phases we considered the quasi-stationary system of equations, which is reduced to a nonlinear second-order equation of parabolic type. The peculiarity of this equation is its possible degeneracy on the solution. The small parameter at the highest derivative greatly complicates the study of initial-boundary problems. Numerical calculations were performed using the implicit finite-difference scheme.