  Motivated by recent observations of deuterated molecules in the interstellar
medium, we examine the production of HD and D$_2$ molecules on dust grain
surfaces. A mechanism for the enhanced production of these deuterated molecules
is studied. This mechanism applies on grain surfaces on which D atoms stick
more strongly than H atoms, under conditions of low flux and within a suitable
range of temperatures. It is shown that under these conditions the production
rates of HD and D$_2$ are greatly enhanced (vs. the H$_2$ production rate)
compared with the expected rates based on the adsorption of gas-phase atomic
abundances of D and H. The enhancement in the formation rate of HD is
comparable with the enhancement due to gas-phase ion-molecule reactions in
diffuse clouds.
