In a few preceding studies several different non-steady problems for lubricated contacts were studied. It was determined that the initial conditions of the system different from the corresponding values for a steady lubricated contact cause decaying oscillations of the system. The general problem of the possible responses of the system to small excitation was never formulated and studied. Therefore, there is a certain value in knowing the response of a lubricated contact to small external disturbances. To learn that one has to determine the eigenvalues of the particular lubricated system. This problem is formulated and studied here. A slightly perturbed condition of a steady state for a lightly loaded lubricated contact is considered. The problem is linearized about its steady solution and the eigenvalues of the non-steady linear system describing the perturbations of the steady state are found. The general approach when the elastic surface displacements are taken into account is described. To simplified the problem and to obtain an analytical solution of the problem the case of rigid solid materials and constant viscosity is considered. Two cases of the problem are analyzed: (a) when the external force applied to the solids is artificially maintained constant and equal to the cumulative force produced by the contact pressure (b) the bottom solid position is fixed in space and cannot move while the upper solid of a specific mass can move in the direction of the applied external force due to the difference between the applied external force and cumulative force produced by contact pressure. In both cases the equations for the eigenvalues of the system, i.e. the complex frequencies are determined. In both cases the asymptotic and numerical analysis of the complex frequencies is conducted and the oscillation frequencies and rates of decay are determined and represented graphically.