Abstract. We prove that up to isomorphism, the number of regular hamiltonian embeddings of K_n,n is 2 or 1, depending on whether n is a multiple of 8 or not. We also show that for each n there is, up to isomorphism, a unique regular triangular embedding of K_n,n,n. Here, a 2-cell embedding of a graph in a surface (orientable or not) is regular if the automorphism group of the embedding acts transitively, and hence regularly, on the flags (incident vertex-edge-face triples). The proofs are group-theoretic ones.