The problem of robust stability is considered for mechanical systems described by Lienard differential equations with pointwise or distributed delays, where all nonlinearities are homogeneous functions of different degrees. To this end, qualitative stability conditions are derived for an auxiliary delay-free system, and next they are used to construct different Lyapunov–Krasovskii functionals for delayed counterparts. The influence of time-varying perturbations is investigated using the averaging theory. The focus is put on importance for robustness of a mild relation between the homogeneity degrees. The rates of convergence for the solutions are evaluated. The results are illustrated by simulations for an academic example.