A local level-set concept for front tracking on arbitrary grids. This paper proposes a general multi-dimensional front tracking concept for arbitrary physical problems. The tracking method is based on the level-set approach with a restricted dynamic definition range in the vicinity of the fronts. Special attention is drawn to the classical level-set method, i.e., accuracy issues and topological restrictions. In this concern, a less sensitive time integration is introduced, and the problem of interacting discontinuities is addressed. The concept is integrated in the basic modular finite volume solution package MOUSE for systems of conservation laws on arbitrary grids.