For over a century the relationships between the four major groups of the phylum Arthropoda (Chelicerata, Crustacea, Hexapoda and Myriapoda) have been debated. Recent molecular evidence has confirmed a close relationship between the Crustacea and the Hexapoda, and has included the suggestion of a paraphyletic Hexapoda. To test this hypothesis we have sequenced the complete or near-complete mitochondrial genomes of three crustaceans (Parhyale hawaiensis, Squilla mantis and Triops longicaudatus), two collembolans (Onychiurus orientalis and Podura aquatica) and the insect Thermobia domestica. We observed rearrangement of transfer RNA genes only in O. orientalis, P. aquatica and P. hawaiensis. Of these, only the rearrangement in O. orientalis, an apparent autapomorphy for the collembolan family Onychiuridae, was phylogenetically informative.We aligned the nuclear and amino acid sequences from the mitochondrial protein-encoding genes of these taxa with their homologues from other arthropod taxa for phylogenetic analysis. Our dataset contains many more Crustacea than previous molecular phylogenetic analyses of the arthropods. Neighbour-joining, maximum-likelihood and Bayesian posterior probabilities all suggest that crustaceans and hexapods are mutually paraphyletic. A crustacean clade of Malacostraca and Branchiopoda emerges as sister to the Insecta sensu stricto and the Collembola group with the maxillopod crustaceans. Some, but not all, analyses strongly support this mutual paraphyly but statistical tests do not reject the null hypotheses of a monophyletic Hexapoda or a monophyletic Crustacea. The dual monophyly of the Hexapoda and Crustacea has rarely been questioned in recent years but the idea of both groups' paraphyly dates back to the nineteenth century. We suggest that the mutual paraphyly of both groups should seriously be considered.