Double homeobox (DUX) genes are unique to eutherian mammals and normally expressed transiently during zygotic genome activation. The canonical member, DUX4, is involved in facioscapulohumeral muscular dystrophy (FSHD) and cancer, when misexpressed in other contexts. We evaluate the 3 human DUX genes and the ancestral single homeobox gene sDUX from the non-eutherian mammal, platypus, and find that DUX4 activities are not shared with DUXA or DUXB, which lack transcriptional activation potential, but surprisingly are shared with platypus sDUX. In human myoblasts, platypus sDUX drives cytotoxicity, inhibits myogenesis, and induces DUX4 target genes, particularly those associated with zygotic genome activation (ZGA), by binding DNA as a homodimer in a way that overlaps the DUX4 homeodomain crystal structure. DUXA lacks transcriptional activity but has DNA-binding and chromatin accessibility overlap with DUX4 and sDUX, including on ZGA genes and LTR elements, and can actually be converted into a DUX4-like cytotoxic factor by fusion to a synthetic transactivation domain. DUXA competition antagonizes the activity of DUX4 on its target genes, including in FSHD patient cells. Since DUXA is an early DUX4 target gene, this activity potentiates feedback inhibition, constraining the window of DUX4 activity. The DUX gene family therefore comprises cross-regulating members of opposing function, with implications for their roles in ZGA, FSHD, and cancer.