A problem of identification of the heat transfer sources in nonlinear media is considered with account for the time of heat flux relaxation. In order to solve the identification problem we use the approach based on the theory of inverse infinite-dimensional open dynamical systems (DS) or, in other words, input-state-output systems. For solving the identification problems we used finite-difference methods. The results of numerical simulation of the problems of internal heat sources identification in nonlinear hyperbolic or parabolic equation are presented. (C) 2015 Elsevier Ltd. All rights reserved.