His main work concerned the investigation of interstitial fauna and the exposition of a phylogenetic system for the animals.
Peter Ax attended the Oberschule für Jungen in Hamburg until 1944 and subsequently completed his military service.
Peter Ax worked primarily on the micro- and meiofauna of the interstitial environment in marine sediments, and on the systematics of flatworms.
He described an array of hitherto unknown species from this environment, including Diplosoma micans, the first tunicate to be found in the interstitial habitat, in 1970.
He was a member of the Akademie der Wissenschaften und der Literatur in Mainz, a fellow at the Institute for Advanced Study, Berlin in 1986/87, and an honorary member of the Gesellschaft für Biologische Systematik.