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Mickens (1981, 1984) has considered analytic techniques for obtaining approximate solutions to one-dimensional nonlinear oscillatory systems x(double-dot) + x = lambda f(x, x/dot/, lambda) where lambda is a small positive parameter and f is a nonlinear polynomial function of its arguments. However, in certain cases there is interest in the analysis of physical systems for which the nonlinear function f(x, x/dot/, lambda) is singular for finite values of x or x(dot). The present investigation is concerned with the use of existing approximate analytic schemes to obtain solutions to singular nonlinear oscillatory differential equations.