The invention relates to mice having functionally silenced endogenous lambda (.lamda.) and kappa (.kappa.) L-chain loci, comprising antibody-producing cells in which the C.sub.H1 domain is functionally silenced, either via spontaneous processes in somatic antibody-producing cells or due to germline deletion of the C.sub.H1 domain. Mice of the invention are capable of producing H-chain-only antibody lacking a functional C.sub.H1 domain; transgenic human heavy-chain-only antibodies lacking a functional C.sub.H1 domain can be produced following insertion into the mouse of an artificial locus with human heavy chain V, D and J segments and a constant region, which is preferably a modified constant region with alterations in, around or upstream of a C.sub.H1 domain and/or removal of a C.sub.H1 domain.