We consider a metamaterial possessing nonlinear magnetic response owing to nonlinear electronic components inserted into resonant conductive elements. We imply that the insertions operate in an essentially nonlinear regime, so that a nonlinear magnetic susceptibility cannot be introduced and separate analysis is required for different nonlinear processes. Here we develop an approach for analyzing three-wave coupling processes with a strong pump wave and two weak signals. We discuss the peculiarities of coupling arising from use of insertions with variable resistance or variable capacitance. We estimate that extremely strong nonlinear coupling can be achieved using typical diodes reported in the literature.