Abstract: The invention provides methods and compositions for generating non-human transgenic cells and organisms that are transgenic at one or more gene sequences by separately recombining fragments of a complete gene in temporal sequence. According to the methods of the invention, a set of DNA constructs containing a non-endogenous DNA sequence flanked and/or operably linked at its ends by sequences from the non-human organism are generated by recombination in a bacterial cell, for example, in E. coli. The DNA constructs that are produced can then be introduced into a non-human homologous recombination competent cell where successive cells will contain recombined segments of a target gene, with the ultimate cell in a line containing an endogenous target gene completely replaced by genomic DNA of another species.