Stability analysis methods and stabilizing controls for nonlinear nonautonomous mechanical systems are discussed. Theorems on stability of equilibrium positions in the case of essentially nonlinear positional forces are proved on the basis of decomposition of systems under study. Time estimates for transient processes are found, and the effect of nonstationary perturbations on stability of equilibrium positions is studied. The results obtained are used for solving stabilization problem for mechanical systems with regard to the structure of control forces. Situations where stabilizing controls can be constructed are determined, and the nonlinear forces that play the key role in these situations are identified.