Recently observed high harmonic multi-particle echo resonances (multiple quantum coherence) in NMR have been interpreted using either direct coupling or local-field mechanisms. We show that a unified picture for both mechanisms may be obtained by calculating the signals perturbatively in the incoming pulses in terms of response functions using a many-body approach originally developed for nonlinear optics. Specific signatures which can distinguish between the two are identified, and new double quantum resonances of both types are predicted in four-wave mixing in the direction k(1) + k(2) - k(3). (C) 2002 Elsevier Science B.V. All rights reserved.