It has been suggested that NaH may be detectable in diffuse interstellar clouds. We discuss the photodissociation process of NaH and calculate the rate of destruction by the interstellar radiation field. In the unshielded field, the mean lifetime is about 10 years. There appears to be no efficient gas-phase mechanism for the production of NaH. If it is produced with high efficiency on grain surfaces, abundances of order 10/sup 10/ cm/sup -2/ can be achieved. For LiH, a similar analysis leads to an upper limit of 10/sup 6/ cm/sup -2/.