Stability boundaries from approximate characteristic equations of a class of feedback systems with rapidly varying periodic parameters are obtained, using impulse techniques with the iterated feedback method (Prasada Kao 1970), while the rapidly varying parameter is suitably approximated as a. modulated train of impulses. The predicted results are compared with the experimental observations in the case of a typical third-order system with a rapidly varying parameter (Clark el al. 1964). The method is used to obtain approximately the stability of certain coupled systems.