We discuss various systems of inbreeding, by artificial insemination, with the object of producing a pure line of honey-bees. It is shown that mother-son mating, if practicable, is easily the most efficient system. Brother-sister and aunt-nephew mating systems are also possible, but much slower. They may, however, be easier to work in practice. There is yet not much information as to what extent it is possible to obtain pure lines of bees by inbreeding.