Abstract-In the paper, the deep evolving neural network and its learning algorithms (in batch and on-line mode) are proposed. The deep evolving neural network's architecture is developed based on GMDH approach (in J. Schmidhuber's opinion it is historicaly first system, which realizes deep learning ) and least squares support vector machines with fixed number of the synaptic weights, which provide high quality of approximation in addition to the simlicity of implementation of nodes with two inputs. The proposed system is simple in computational implementation, characterized by high learning speed and allows processing of data, which are sequentially fed in on-line mode. The proposed system can be used for solving a wide class of Dynamic Data Mining tasks, which are connected with nonstationary, nonlinear stochastic and chaotic signals. The computational experiments are confirmed the effectiveness of the developed approach.