The analysis of complex chemical reaction systems isfrequently complicated because of the coexistence of fastcyclic reaction sequences and slower pathways that yield anet production or destruction of a certain species ofinterest. An algorithm for the determination of the lattertype of reaction sequences (in a given reaction system) ispresented. Under the assumption that reaction rates areknown, it finds the most important pathways by solving alinear optimization problem for each of them.The application of this algorithm to stratosphericchemistry, in particular the determination of catalyticozone destruction cycles, is illustrated.