The invention relates to a multi-phase transverse flux machine, comprising a stator with substantially U- and I-shaped cores (1, 2) made of a soft-magnetic material and a stator winding (3) for each phase which generates a magnetic flux in said cores, as well as a rotor with a circular magnetic return path (4). The stator phases are magnetically separated from each other. The rotor has electrically conductive material (5, 6) in each phase and the electrically conductive material of at least two phases is positioned in the rotor and interconnected in such a way that when an alternating current flows through the stator windings of said phases a current is induced in the electrically conductive material which generates a starting torque for the rotor. The at least two phases therefore electrically form an induction machine in the rotor. The rotating field can be generated by applying phase-displaced currents to the stator windings of the at least two phases. In addition, the electrically connected rotor poles of the at least two phases and/or the stator poles assigned to same can be geometrically displaced in relation to each other. The transverse flux machine therefore has the performance characteristics of an asynchronous machine so that it can be operated without permanent magnets.