In this paper the stability problem of a low-order non-linear feedback control system is investigated with the help of an r.m.s. describing function. A second-order system incorporating a backlash non-linearity is considered and it is shown that the r.m.s. describing function for the backlash element provides a more reliable locus in predicting the existence of ‘ limit cycle ’ oscillation in the system and in computing the value of the limit cycle parameters.