The following problem is considered: given a system which has tracking/disturbance signals arising from a class of periodic signals with periodT, say, assume that such a periodic signal haspdominant harmonic components contained in {ω1,l = 0, 1,…,v}. Then it is desired to find a finite-dimensional linear controller which gives exact robust asymptotic regulation for the case of sinusoidal signals with frequencies ω1,l = 0, 1,…,v, subject to certain controller gain magnitude constraints and/or gain margin tolerance constraints which may be imposed on the problem. This is called ‘the approximate robust servomechanism problem for periodic signals of the class {ω1,l = 0, 1,…,v}’. It is to be noted that such a problem cannot in general be solved by using high gain control synthesis methods. Existence conditions and a controller design method are given to solve the problem. A number of examples is given to illustrate the type of results that may be achieved.