The development of ontologies involves continuous but relatively small modifications. However, existing ontology reasoners do not take advantage of the similarities between different versions of an ontology. In this paper, we propose a collection of techniques for incremental reasoning -- that is, reasoning that reuses information obtained from previous versions of an ontology. We have applied our results to incremental classification of OWL ontologies and found significant improvement over regular classification time on a set of real-world ontologies.