Default reasoning is computationally expensive. One of the most promising ways of easing this problem and developing powerful implementations is to split a default theory into smaller parts and compute extensions in a modular, “local” way. Up to now this idea was only followed for Reiter's default logic, yet it is also relevant to other variants of default logic which have found increasing recognition in the past years. This paper shows how it can be modified to work for several popular, alternative approaches of default reasoning: justified, constrained and rational default logic. This work defines the formal basis for a Web‐based default reasoning system which is under development at our institution.