It is shown that for the nonstationary equations of motion of the linear viscoelastic fluids, whose defining equation has the form the stationary system is the Navier-Stokes stationary system with viscosity coefficient v: It is proved that for “small” Reynolds numbers the solutions of the initial-boundary value problems for the equations of motion of the Oldroyd fluids (M=L=1, 2, ...) and Kelvin-Voight fluids (M=L + 1, L=0, 1, 2, ...) converge for t→∞ to the solution of the first boundary value problem for the stationary Navier-Stokes system (*).