In this talk, we consider the task of model order reduction (MOR) for a wildland fire model, cf. [1]. The model is described by a partial differential equation for the heat transfer which is coupled via a reaction term to an ordinary differential equation modeling the progress of the chemical reaction. Since the dynamics of the full-order model (FOM) exhibits traveling waves with sharp front profiles, classical linear MOR techniques are not suitable for obtaining fast and accurate reduced-order models (ROMs). Instead, we employ a nonlinear model reduction technique recently introduced in [2]. The approach is based on approximating the FOM state by a linear combination of transformed modes and allows for an effective reduction of transport-dominated systems like the considered wildland fire model. The transformations which are applied to the modes are parameterized by time-dependent path variables which constitute a part of the ROM state. As a consequence, the approximation ansatz is nonlinear and we derive corresponding ROMs via residual minimization. Furthermore, an efficient offline/online decomposition is achieved by introducing an extension of the (discrete) empirical interpolation method which is suitable for transport-dominated systems. The numerical results for the wildland fire model demonstrate that the new approach is able to yield fast and accurate ROMs which outperform classical ROMs based on proper orthogonal decomposition and Galerkin projection.