Abstract. Evolutionary changes in segment number during the radiation of Mecistocephalidae, a group of geophilomorph centipedes with segment number usually invariant at the species level, were explored based on a cladistic analysis of forty-six mecistocephalid species, representative of the extant diversity in segment number. The data matrix included 118 morphological characters. Trends were recognized in the evolution of segment number and discussed in relation to the underlying ontogenetic mechanisms of segmentation. The basic trend was towards an increasingly higher number of leg-bearing segments, from (most probably) forty-one to sixty-five (101 in one exceptional case). Changes always involved even sets of segments. Additions of two, four or eight segments usually occurred, but a case of overall duplication of the whole number was also documented. Most changes occurred starting from values belonging to the arithmetical series forty-one, forty-five, forty-nine, whereas the intermediate values forty-three, forty-seven, fifty-one were often evolutionary dead-ends. This evidence suggests a multiplicative mechanism of segmentation involving one or more final run of duplication, as well as a precise control of the final number of segments which produces absolute number stability, except for a single, highly derived species with an exceptionally high number of segments. These ideas contribute to a more general model of arthropod segmentation recently developed by Minelli. A taxonomic revision of mecistocephalids is presented: three subfamilies are proposed (Arrupinae, Dicellophilinae and Mecistocephalinae) and Sundarrup is recognized as a junior synonym of Anarrup.