The paper presents an overview of studies of the multi-junction (MJ) solar cells (SC) with IV characteristics having nonlinear peculiarities. It is shown that such peculiarities can arise either due to hetero-interface barriers (HB) for majority charge carriers or due to problems with tunnel diodes (TD). It is usually difficult to identify which of these hetero-structural objects is the cause of this nonlinearity, since the peculiarities appear similarly in the IV characteristics of MJ SC. The experimental method presented in this work is based on the study of IV characteristics during the overheating of MJ SCs. The behavior of nonlinear peculiarities caused by an imperfect TD or an HB is fundamentally different during the overheating of SCs, which makes it possible to identify the type of hetero-structural object. Since the number of hetero-interfaces in MJ SC is large, a method determining the position of problematic objects in the MJ structure was also developed. The method is based on the illumination of individual subcells using different laser wavelengths. Both methods considered were tested experimentally on GaInP/GaAs/Ge SCs.