The scope of the paper is to reveal the strange behavior of Direct Torque Controlled (DTC) drives resulting from the nonlinearity of hysteresis comparators. A piecewise-defined, non-stroboscopic, discrete-time Poincaré map can be constructed for the system which takes into account the fast switching operations of the Voltage Source Converter (VSC). The evolution of the stator flux linkage and the electric torque within the hysteresis loops are determined from switch to switch. The movement of the two controlled state variables exhibits periodic, subharmonic, chaotic and intermittent chaotic states along a special series of border collision bifurcations induced by discontinuity of the Poincaré mapping function. In order to give a better insight into these bifurcations, a one-dimensional piecewise linear discontinuous iterated map is developed and analyzed.