In this work, we present a simple kinetic model of horizontal gene transfer. It describes the processes of gene duplication, mutation, gene transfer and the regulation of the total size of the genome for genetically homogeneous prokaryotic species or strains. The emerging nonlinear system of first-order differential equations can be linearized at the stationary point. For selected models, we give an analytical solution for the number of foreign and native genes within a species. We identify a regime characterized by a fast gene transfer rate and species with a mixed genome, a slow gene transfer regime with pure organisms, and a crossover region. The data are compared to experiments, and the biological implications of our model are discussed.