When the output of a complex chemical model is analysed, a typical topic is the determination of pathways, i.e. reaction sequences, that produce or destroy a chemical species of interest.A representative example is the investigation of catalytic ozone destruction cycles in the stratosphere.An algorithm for the automatic determination of pathways in any given reaction system is presented.Under the assumption that reaction rates are known, it finds all significant pathways, i.e. all pathways with a rate above a prescribed threshold.The algorithm forms pathways step by step, starting from single reactions.The chemical species in the system are consecutively considered as `branching points'.For every branching-point species, each pathway producing it is connected with each pathway consuming it.Rates proportional to `branching probabilities' are calculated.Pathways with a rate that is smaller than a prescribed threshold are discarded.If a newly formed pathway contains sub-pathways, e.g. null cycles, it is split into these simpler pathways.In order to demonstrate the performance of the algorithm, it has been applied to the determination of catalytic ozone destruction cycles and methane oxidation pathways in the stratosphere.