Aftereffect measurements have been performed on synthetic ferrimagnets showing strong perpendicular magnetic anisotropy, namely (Co/Pt)/Ir/(Co/Pt), by measuring the magnetization of the sample as a function of time for several different applied magnetic fields. Unexpected magnetic relaxation has been observed. Indeed, for some particular applied magnetic fields, the magnetization as a function of time first plummets and then increases. This nonmonotonic aftereffect can be understood by considering the possible magnetic states and the transitions between those states. This understanding has been confirmed and detailed using magneto-optical Kerr effect (MOKE) microscopy. Indeed, the measurements show nucleation and propagation of a transient metastable magnetic configuration. Furthermore, we were able to obtain a good qualitative agreement between a simple one-dimensional model and the experimental observation. We could strongly support the hypothesis that this peculiar nonmonotonic behavior could be a very general feature that should be observed in any antiferromagnetically coupled system (synthetic ferrimagnets, synthetic antiferromagnets) with perpendicular magnetic anisotropy.