Dynamics of nonlinear coupled driven oscillators is investigated. Recently, we have demonstrated that the amplitude profiles – dependence of the amplitude A on frequency Ω of the driving force, computed by asymptotic methods in implicit form as FA,Ω=0, permit prediction of metamorphoses of dynamics which occur at singular points of the implicit curve FA,Ω=0. In the present study we strive at a global view of singular points of the amplitude profiles computing bifurcation sets, i.e. sets containing all points in the parameter space for which the amplitude profile has a singular point. •The effective equation for coupled nonlinear Duffing equations is investigated.•Implicit equations for amplitude profiles of nonlinear resonances are studied.•The bifurcation manifold in the parameter space is computed.•Examples of metamorphoses of dynamics at singular points are presented.•The method can be applied to other dynamical systems.