Abstract. The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the second one based on iso-parametric finite elements in both the static and moving parts. The coupling is obtained by means of the mortar element method (see [7]) and the approximation on the whole domain turns out to be non-conforming. In both cases optimal error estimates are provided. Numerical tests are then proposed in the case of standard first order finite elements to test the reliability and precision of the method. An application of the method to study the influence of the free part movement on the currents distribution is also provided.Mathematics Subject Classification. 35Q60, 65N15, 65M55, 68U20, 78A30.