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We present the results on current-induced magnetic dynamics in a single magnetic tunnel junction consisting of a thick magnetic layer separated by a tunnel barrier from a thin free magnetic layer. Both in-plane and out-of-plane torque components have been taken into account and both turned out to be important for description of magnetic switching and magnetic dynamics. The torque components have been calculated in the framework of spin polarized one-band free-electron-like model. The interlayer exchange coupling between magnetic layers through the tunnel barrier has also been taken into account. To describe current-induced dynamics, the calculated spin torque has been included into the phenomenological Landau-Lifshitz-Gilbert equation.