The method of strained coordinates is a technique for dealing with certain types of nonuniformities which occur in asymptotic expansions. In this chapter two related methods will be described, namely the Lindstedt–Poincaré 3 and the Lighthill 4 techniques. The former applies to systems which are periodic where the period of the motion is changed by a perturbation. It can be applied to various oscillators such as mechanical spring and mass systems, electrical systems and planetary motion.