The paper deals with responses of a non-linear multiple lumped dynamical system bounded in a large neighbourhood of the single, asymptotically stable equilibrium point. The sufficient, analytic criteria for the non-oscillation of such responses have been introduced in previous work (cf. Skowronaki and Shannon 1972). On the basis of the latter, the author discusses a geometric interpretation of necessary and sufficient criteria for non-oscillatory responses applied to the synthetic design of the relevant systems