An investigation, using optical microscopy and SEM, of the trunk limbs of the Anomopoda has revealed a large number of characters, previously underused or unused in taxonomy and comparative morphology. All these characters, which are nicely paralleled by some more conventional traits (head shield and pores, postabdomen, antennae ...), show one clear tendency across all groups studied: a state of complexity at one extreme, and a state of often incisive simplification at the other extreme, with a number of transitional stages in between. The complex character state, which itself is a simplification of the leg structure of the Ctenopoda and other, ‘large’ Branchiopoda, is here considered to represent a primitive condition. The simplified state is considered advanced. Based on this assumption, we list a number of unifying characters (mainly structural aspects of P1 and P2, but also the gnathobase of P3 and P4) for all macrothricid and chydorid-like anomopods, which we unite in the new suborder Radopoda. Non-radopod Anomopoda are not reclassified. We then derive a cascade of (mainly trunk-limb based) characters to work out a hypothesis on the evolution of the Radopoda. The ‘chydorid’ line (basically the former family Chydoridae) is classified as a superfamily (the Eurycercoidea), with three families; the ‘macrothricid’ line is capped by the superfamily Macrothricoidea, with four families. Of these seven families, four are upgraded from subfamily status, the Chydoridae are left status quo, the Macrothricidae are redefined, and the Neothricidae are a new family. The Macrothricidae are further subdivided in two subfamilies, of which the Macrothricinae appear reasonably homogeneous (monophyletic), while the non-Macrothricinae require further study. Some of these (e.g. Guernella) have almost completely lost their P5, a situation parallel to that of the P6 in the Eurycercidae, Acantholeberidae, and Ophryoxidae.