Because of a serial arrangement of supposed pedal muscles and its high-conical shell, Hypseloconus from the Late Cambrian to Early Ordovician of North America is generally believed to be a monoplacophoran relative of cephalopods. The distinctive pattern of muscle attachments and shell form indicates its close relationship to roughly coeval Siberian Kirengella and several other genera classified in the order Kirengellida. Newly collected material from the Early Ordovician of Siberia shows that the bivalved Angarella, with its ventral valve cementing to a hard substratum, is closely similar to Kirengella and Hypseloconus in the arrangement of shell muscles. Permanently fixed to its substratum was also another probable member of the group, Pygmaeoconus. Musculature of Angarella in some aspects resembles that of the Early Cambrian mobergellans with phosphatic shells, but in the calcitic shell structure it is similar to the craniopsid brachiopods. Irrespective of whether the kirengellids are brachiopods or not, they should be removed from considerations on the ancestry of cephalopods. The alternative to Hypseloconus as a candidate for cephalopod ancestry is the Early Cambrian Turcutheca, an enigmatic mollusk with endogastrically curved and laterally compressed conch and relatively large subspherical embryonic conch, in both aspects resembling the earliest ellesmeroceratid nautiloids.