To study perturbation problems of differential equations it is essential to use our knowledge of the ‘unperturbed’ problem. An example using the Mathieu-equation shows erroneous results arising from crude averaging. Variational equations suitable for averaging can be obtained from amplitude-phase variables, comoving variables, amplitude-angle transformation and forced linear equations. Contraction and iteration approximations prepare the way for use of the Poincaré-Lindstedt method. Various perturbation methods are discussed showing the advantages of averaging.