Arbitrary Lagrangian Eulerian (ALE) methods provide a well established basis for the numerical analysis of rolling contact problems, the theoretical framework is well developed for elastic constitutive behavior. Special measures are necessary for the treatment of history dependent and explicitly time dependent material behavior within the relative–kinematic ALE– picture. In this presentation a fractional step approach is suggested for the integration of the evolution equation for internal variables. A Time–Discontinuous Galerkin (TDG) method is introduced for the numerical solution of the related advection equations. The advantage of TDG–methods in comparison with more traditional integration schemes is studied in detail. The practicability of the approach is demonstrated by the finite element analysis of rolling tires.