The deuteron production by the nucleon bombardment is discussed in detail. First in §2, according to the general theory of nuclear reactions developed by Ui, the transition matrix is written as the sum of two elements, which correspond to the compound and the noncompound nuclear processes. In the processes proceeding through the compound nucleus, the indirect pickup process, in which a neutron emerging from the compound nucleus picks up any proton, gives a larger yield than the deuteron evaporation in the usual sense. The average kinetic energy of deuterons thus produced is about three times larger than that in the Maxwellian type (§3). In the direct pickup process of low energy (p; d) reaction, the Coulomb effect is found to play an important role and the remarkable backward maximum in the angular distribution of the reaction product is predicted (§4). Direct pickup process at moderate and high energies is calculated by the Born approximation, assuming the Gaussian momentum distribution for the tail of the wave function of the nucleon to be picked up. The forward peak in the angular distribution for sharp energy deuteron groups corresponding to the ground state and the low-lying levels is interpreted in terms of the direct process taking place in the external region of the target nucleus (§5). In the limiting case of the weak coupling, which is an appropriate approach to the high energy reaction, the calculation is performed along the Chew-Goldberger's procedure on the basis of the non-degenerate Fermi gas model and the total cross section is found to obey approximately 1/v-law (§6). Further the production cross section of 1s deuterons is evaluated in the same way, and is found to give a contribution comparable to the production of deuterons in the ground state (§7). Main conclusions obtained in the present work are summarized in §8.