A density matrix description of coupled spin systems in the presence of two strong rf fields is given following a relaxation matrix formalism. The irradiating rf field, H2, has significant effects on the population distribution in a spin system even though the frequency of H2 is not close to a resonance frequency of the system. Signal frequencies and intensities calculated in the limit of large amplitudes of the observing field H1 with ω2 off resonance and ω1 saturating only a single line are compared with experimental proton—fluorine field-sweep nuclear magnetic double resonance spectra of CHFCl2 and CH2F2. Apart from relaxation effects, the most important factor affecting the saturated intensities is the mixing of the pure states by H2.