A fully analytical description of the control of the cross-correlated cross relaxation of multiple-quantum coherences in the presence of local dynamics under heteronuclear double-resonance radio-frequency (RF) irradiation is presented. The contribution of chemical exchange to relaxation can be partly or fully quenched by RF fields. We assume a correlated two-site chemical exchange model with arbitrary populations, and show that in the limit of fast exchange the dependence of the effective multiple-quantum cross-relaxation rate on the applied RF amplitude can be described by a compact analytical expression. Numerical simulations and preliminary experiments support our theoretical results. The relaxation dispersion as a function of RF amplitude can provide accurate information on the kinetics of correlated processes.