The problem considered is the stability of multi-variable feedback systems having several, possibly time-varying, non-linear elements. No specific structure is assumed and the problem is formulated in terms of a matrix transfer function G(s) of the linear part of the system. Several examples of different structures are given with the corresponding form of G(s). The stability criteria illustrated are extensions of the Popov criterion to the multi-variable case which have been proved elsewhere. Examples are given for which improved results are obtained in a more simple and straightforward manner than those obtained previously.