The analysis of complex chemical reaction systems is frequently complicatedbecause of the coexistence of fast cyclic reaction sequences and slower pathwaysthat yield a net production or destruction of a certain species of interest.An algorithm for the determination of both these types of reaction sequences (ina given reaction system) is presented. Under the assumption that reaction ratesare known, it finds the most important pathways by solving a linear optimizationproblem for each of them.This algorithm may be used as a tool for the interpretation of chemical modelruns.For illustration, it is applied to examples in stratospheric chemistry,including the determination of catalytic ozone destruction cycles.