The paper considers the problem of designing Adaptive Feedforward Control (AFC) systems for uncertain SISO linear systems perturbed by multi-sinusoidal disturbances of known frequencies. The proposed approach removes the longstanding assumption that either the sign of the real part or the imaginary part of the transfer function of a stable plant at the frequency of excitation be known for AFC to be applicable, which is referred to in this paper as an SPR-like condition. Notable features of the solution are that persistence of excitation is not required and stability analysis tools based on averaging are avoided; hence, the requirement of an exponentially stable equilibrium for the closed-loop system is circumvented.