The production of deuterium, He3, lithium, beryllium, and boron by galactic cosmic rays in the interstellar medium, over the life of the Galaxy, is calculated. It is found that high-energy α-α reactions contribute in an essential way to the observed lithium. When allowance is made for the interchange of material between stars and the interstellar gas and for the change of cosmic-ray intensity with time, the Li6, Be9, and boron produced turn out to be ample to explain the observed abundances, and with remarkable internal consistency. Deuterium and He3 arenot produced in significant amounts, nor Li7 in sufficient amount, however. To explain the Li7/Li6 ratio measured terrestrially and in chondritic meteorites, we invoke cosmological production of Li7. This implies the production of deuterium, He3, and He4 as well, in amounts consistent with observation. The theory in its present form cannot explain a solar-system Li7/Li6 ratio of 12and stellar ratios as low as 3, but additional processes can be adduced to reconcile them. The consistency of the numbers when cosmological production is included lends additional support to the big-bang hypothesis. An incidental result is that the mean luminosity of the Galaxy over its lifetime has been about 3 times its present luminosity.