Being able to extend an OWL ontology with some form of rules is a feature that many ontology developers consider as very important. Nevertheless, working with rules in practice can be difficult since the tool support is not as good as for handling standard ontologies. Furthermore, the existing rule syntaxes are not very well aligned with the new OWL 2 standard. We propose, therefore, an extension to OWL 2 for representing rules, which is directly inspired by (DL Safe) SWRL rules, but uses and extends the succinct and human-readable functional-style syntax of OWL 2. We also propose an OWL/XML version of the syntax for easy XML serialization. Support for parsing such rules has been added to the new OWL API 3.0 and reasoning support is available in the two OWL 2 reasoners Pellet and HermiT. In HermiT, these rules can also be used in conjunction with description graphs.