Abstract: A class of isochronous oscillatory systems in the plane subject to the influence of combined parametric and external perturbations is considered. It is assumed that the intensity of perturbations decays with time, and the frequency satisfies a resonance condition. The emergence of resonant solutions with infinitely growing amplitude, as well as trajectories tending to the equilibrium of the limiting system, is discussed. The conditions that guarantee the existence and stability of such regimes are described.