Serine integrases, DNA site-specific recombinases used by bacteriophages for integration and excision of their DNA to and from their host genomes, are increasingly being used as tools for programmed rearrangements of DNA molecules for biotechnology and synthetic biology. A useful feature of serine integrases is the simple regulation and unidirectionality of their reactions. Recombination between the phage attP and host attB sites is promoted by the serine integrase alone, giving recombinant attL and attR sites, whereas the 'reverse' reaction (between attL and attR) requires an additional protein, the recombination directionality factor (RDF). Here, we present new experimental data on the kinetics and regulation of recombination reactions mediated by ϕC31 integrase and its RDF, and use these data as the basis for a mathematical model of the reactions. The model accounts for the unidirectionality of the attP × attB and attL × attR reactions by hypothesizing the formation of structurally distinct, kinetically stable integrase-DNA product complexes, dependent on the presence or absence of RDF. The model accounts for all the available experimental data, and predicts how mutations of the proteins or alterations of reaction conditions might increase the conversion efficiency of recombination.