In this paper we summarize the major element chemical variation for basalts from the Deep Sea Drilling Project Leg 37 and relate it to stratigraphic position in each of five drilling sites. Least-squares techniques are successfully used to quantify the nature and extent of alteration in these basalts, and to correct the major element analysis back to a magmatic, or alteration-free, composition on the assumption that alteration takes place in two ways: (1) secondary minerals are introduced into veins and vesicles, and (2) CO2 and H2O react with components in the rock to form a simple alteration assemblage. A chemical stratigraphy is defined for these basalts by grouping lavas whose chemistries are related by low-pressure phenocryst-liquid differentiation as identified by least-squares calculation. Major chemical-stratigraphic units are as much as 200 m thick; correlations of these units can be made between the holes at site 332 (about 100 m apart), but not between the other sites. Compositions of parental magmas are calculated by extrapolating low-pressure variations to a constant value of 9% MgO. The differences in these extrapolated compositions reflect high-pressure processes, and suggest that clinopyroxene may be an important phase in either intermediate-level fractionation of basaltic liquids, or as a residual phase during the partial melting which produces these basaltic liquids. Several of the basaltic liquids calculated as parental to the Leg 37 basalts have CaO contents greater than 14% and indicate that the oceanic mantle is richer in CaO and Al2O3 than values used in pyrolite models for the upper mantle. A model for magma generation and eruption beneath the Mid-Atlantic Ridge embodies the following characteristics: 1. (1) Separate magma batches are generated in the mantle. 2. (2) Each of these may be erupted directly or stored at shallow depth where significant fractionation takes place. Common fractionation processes are inferred to be gravitative settling of olivine, flotation (?) of plagioclase, and flow differentiation of an olivine-plagioclase-augite assemblage. 3. (3) Eruption of fractionated lava derived from earlier magma batches may alternate with eruption of younger less-fractionated or unfractionated magma. ?? 1978.