Objective: Intra-axiom redundancies are elements of concept definitions that are redundant as they are entailed by other elements of the concept definition. While such redundancies are harmless from a logical point of view, they make concept definitions hard to maintain, and they might lead to content-related problems when concepts evolve. The objective of this study is to develop a fully automated method to detect intra-axiom redundancies in OWL 2 EL and apply it to SNOMED Clinical Terms (SNOMED CT). Materials and methods: We developed a software program in which we implemented, adapted and extended readily existing rules for redundancy elimination. With this, we analysed occurence of redundancy in 11 releases of SNOMED CT (January 2009 to January 2014). We used the ELK reasoner to classify SNOMED CT, and Pellet for explanation of equivalence. We analysed the completeness and soundness of the results by an in-depth examination of the identified redundant elements in the July 2012 release of SNOMED CT. To determine if concepts with redundant elements lead to maintenance issues, we analysed a small sample of solved redundancies. Results: Analyses showed that the amount of redundantly defined concepts in SNOMED CT is consistently around 35,000. In the July 2012 version of SNOMED CT, 35,010 (12%) of the 296,433 concepts contained redundant elements in their definitions. The results of applying our method are sound and complete with respect to our evaluation. Analysis of solved redundancies suggests that redundancies in concept definitions lead to inadequate maintenance of SNOMED CT. Conclusions: Our analysis revealed that redundant elements are continuously introduced and removed, and that redundant elements may be overlooked when concept definitions are corrected. Applying our redundancy detection method to remove intra-axiom redundancies from the stated form of SNOMED CT and to point knowledge modellers to newly introduced redundancies can support creating and maintaining a redundancy-free version of SNOMED CT.