The characteristics and properties of a resonant nearly degenerate four-wave mixing signal are studied in the frequency space defined by the pump- and probe-field frequencies. Simultaneous effects of the intense pump field (perturbative treatment at all orders in the amplitude of the total field), chemical concentration of the solution, inhomogeneous distribution of resonance frequencies, and propagation of the electromagnetic fields are studied. Discussion and interpretation of the results are based on different characteristics of the non-linear signal within the absorptive and saturative regime, and on the behaviour in the frequency space of the component of the propagation-vector mismatch. Results obtained in this model are compared to previous spectral homogeneous-line results and to local cases. © 1994, IOP publishing Ltd.