For a class of weakly nonlinear autonomous systems exhibiting both resistive and reactive nonlinearities, asymptotic orbital stability is investigated through a new narrow-band differential approach. The main result is the derivation of the exact characteristic polynomial associated with the local dynamics of the amplitude and phase of the free-running oscillation to be tested. For annth-order circuit, (n– 1) necessary and sufficient stability conditions are then obtained, in an analytical explicit form suitable for computer implementation, by resorting to conventional Hurwitz test algorithms. A comparison with other differential stability criteria available in the literature is also carried out. As an example, a double-tuned oscillator is finally investigated.