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In this paper a developed evolutionary algorithm (NEvA) for simultaneous connections and weights of neural network training is described. A distinctive feature of the algorithm is flexible and effective evolutionary search and a balanced resulting neural network structure due to adaptive mutation operator. In NEvA neural network structure changes, caused by mutation operator, as well as mutation rate are defined independently for each individual. Two different problems are chosen to test the algorithm. The first one is a simple 2-bit parity problem, well known as XOR problem, and the second is a neurocontrol problem of 1 and 2 poles balancing. A comparison of obtained results with results of other algorithms is presented.