The paper addresses to the stability analysis of some classes of nonlinear time-delay systems. Both cases of constant and cases of distributed delays are studied. Using the Lyapunov direct method, sufficient conditions of polystability by nonlinear homogeneous approximation are derived. In addition, the obtained results are extended to the scenario where a system of the first approximation is linear with respect to one part of state variables and nonlinear homogeneous with respect to another one. Some examples of applications of the proposed approaches to the stability analysis of mechanical systems are provided.