We present a model for the evolution of the light-nuclide abundances in the Galaxy, aimed especially at interpreting the observed beryllium and boron abundances as a function of that of iron. We present two models, one for the Galactic halo and the other for the Galactic disk. The main characteristics of the halo model are (1) the relatively rapid change in the physical conditions, on a timescale of less than 2 Gyr, because of the exponentially increasing flow of gas from the halo to form the Galactic bulge---after this period, less than 30% of the initial gas remains in the halo, and star formation there is brought to a halt; (2) the low inferior mass limit for the initial mass function (ml = 0.01), implying that ~60% of the mass that condenses into massive bodies takes the form of substellar objects (masses <=0.1 M&sun;). With these assumptions, we can explain the abrupt increase in the observed metallicity distribution of halo stars near [Fe/H] = -1.7, the evolution of [O/Fe], 4He/H, [N/Fe], and 12C/13C versus [Fe/H], and that of [C/O] versus [O/H], and give an account of [Fe/H] as a function of time, during the halo phase. The main characteristics of the disk model are (1) a timescale of order 15 Gyr and (2) an exponentially increasing infall of gas with very low metallicity. With these assumptions, we can explain the prominent peak in the observed metallicity distribution of disk stars near [Fe/H] = -0.4, the evolution of [O/Fe], 4He/H, [N/Fe], and 12C/13C versus [Fe/H], and that of [C/O] versus [O/H] and also give a good fit to observed [Fe/H] as a function of time. The production of light elements (D, 3He, 6Li, 7Li, 9Be, 10B, and 11B) occurs principally via Galactic cosmic ray (GCR) reactions for all nuclides except deuterium and 3He. Differences between the halo and the disk are (1) a flatter GCR energy flux spectrum and (2) more GCR flux at early epochs (halo) than more recently (disk), as a result of better GCR confinement, both conditions first suggested by Prantzos, Casse, & Vangioni-Flam. A significant contribution of the present paper is to explain the almost linear dependence of 9Be on Fe (or on O) at very low metallicities: the observations show a more nearly linear than quadratic dependence, without requiring the very high local cosmic-ray fluxes implied by the explanation of Feltzing & Gustafsson of spallation close to supernovae. The explanation is that exponentially increasing outflow of gas from the star-forming zone implies the presence of more star-forming gas at very low metallicities ([Fe/H] ~ -3.0). The low inferior mass limit taken here in the initial mass function implies a reduction in the predicted relative number of high-mass stars formed. These conditions, together with the increasing yields of carbon for stars of intermediate and low mass at low metallicities, while the metallicity indicators O and Fe were being produced mainly in massive stars, cause the observed 9Be abundance at very low metallicities, which is enhanced compared with the predictions of models in which 9Be, as a secondary element, depends quadratically on Fe. The exponentially increasing outflow also explains the sharp rise in the abundances of O and Fe and the observed peak in the stellar frequency distribution near [Fe/H] ~ -1.7. A feature of interest in the disk model, due to the exponentially rising infall of non-enriched gas, is the observed loop-back of the 9Be-Fe curve at near-solar metallicity; the 9Be abundance is rising steadily while that of Fe has fallen back.