The selected artificial neural networks were trained and tested to determine the kinetics of theoretically simulated signals for two overlapping independent nucleation-growth processes. Whereas the hybrid convolutional neural network did not perform well, the multilayer perceptron (MLP) showed great potential for the kinetic analysis of complex solid-state reactions and transformation mechanisms. In particular, the MLP architecture exhibited remarkable robustness with respect to the scatter in kinetic data as well as the ability to accurately deal with practically fully overlapping kinetic peaks. When trained on a full spectrum of double-process overlaps, the MLP architecture returned very precise estimates of the kinetic parameters during the testing phase despite the limited data sample used for some of the training. This level of accuracy was observed in the case of both overlapping processes being roughly similarly sized, and for the dominant process in the cases of the two processes being largely disproportionate in magnitude.