This paper introduces direct torque control (DTC) of dual three phase induction machines (DTPIM). In this paper the DTPIM has two, three phase windings spatially shifted by gamma electrical degree that is 30deg or 60deg. DTPIM drive has 64 inverter switching states which provide higher possibility in selecting space voltage vectors than three phase induction machines. In this research we have discussed applying of DTC for two general type of DTPIM with gamma=30 and 60 electrical degrees. According to the presence of the current components which don't any contribution in torque producing, we have shown DTC method isn't applicable for DTPIM with gamma=30deg, but for DTPIM with gamma=60deg we show DTC present acceptable responses. We have validated these methods by simulation results.