This work deals with the behavior of coupled reaction fronts in a novel type of catalytic fixed-bed reactor, the so-called circulation loop reactor. Experiments in a laboratory scale reactor, which are carried out for the oxidation of ethene/methyl chloride mixtures, reveal a complex nonlinear reactor behavior. They motivate the theoretical investigations presented here. In a first step, a simple quasi-stationary wave model is used to study the interaction of two reaction fronts for different values of the kinetic parameters. Then additional effects caused by thermal recoupling in the circulation loop reactor are investigated by a numerical bifurcation analysis of a pseudo-homogeneous model. Different types of react:ion rates are considered and compared with the experimental results. The final aim of the work is to find autothermal operation conditions under which total conversion can be achieved for varying feed compositions, as appear e.g. in waste air treatment.