We study a system of active rotators interacting by short range attractive and long range repulsive coupling. In such systems, one can observe a huge variety of emerging patterns. This includes Turing patterns and coherence-incoherence patterns such as bumps and chimera states. Here, we focus on the transition from stationary to travelling patterns in a drift instability. We elaborate in detail the mathematical framework for a treatment of such states in the continuum limit and present numerical results to discuss the dynamical effects in finite size systems.