Abstract. Experience shows that in systems where process executions are not strictly enforced by process models, often deviations occur. Align-ments between logged process executions and models reveal useful in-sights and can be used for both conformance checking and performance analysis. In this article, we present a memory-efficient approach using marking equations of Petri nets to calculate optimal alignments between process executions and process models. A comparative study shows that in most cases the approach significantly reduces the memory required. This makes it possible to analyze larger logs and models using align-ments. The more deviations exist, the better the approach performs com-pared to the approaches without using marking ...