Glassy to sparsely phyric submarine lavas were recovered from nine Alvin dive sites located along the eastern Galapagos rift and at the intersection with the Inca transform. Samples include quartz-normative tholeitic basalts (MORB), numerous Fe- and Ti-enriched basalt (FeTi basalts) and a smaller number of oceanic andesites (55.9-64.3 wt % SiO2). MORB have light rare earth element (REE) and large ion lithophile (LIL) element depletions but exhibit slight REE fractionation (CeN/YbN 0.6-1.0) and increasing negative Europium anomalies (0.96-0.66) with progressive differentiation. Andesites have sixfold to tenfold enrichments of incompatible elements and volatiles compared to the least fractionated (Mg number <60) basalt recovered. REE and LIL enrichments in the FeTi basalts and andesites are up to 70% greater than those predicted from closed-system fractional crystallization models computed using major and trace element data. Trace element data indicate that extreme fractional crystallization of MORB liquids (40-65.%) have occurred in order for the most evolved FeTi basalt to be generated and further crystallization (40-50%) of FeTi basalt residual liquid is required to produce andesites. Magma mixing has occurred on a small scale in the evolved liquids and can partially explain the chemical characteristics of basaltic andesites. All data point to extensive amounts of fractional crystallization during the evolution of these lavas; however, mantle heterogeneity and other processes such as partial melting, open-system fractional crystallization, and convection-driven thermogravitational diffusion may also play minor roles in influencing magmatic evolution. The principal tectonic controls which influence magmatic evolution along this accretionary boundary are (1) the presence of the cold, thick lithospheric edge of Nazca plate exposed at the intersection with the Inca transform, and (2) attempted rift propagation across the Inca transform intersection, which has resulted in excess magmatism and the eruption of only FeTi basalts. Three subrift, accretionary magmatic domains result from the interplay of transform effects and attempted propagation. The chemistry of lavas is a direct consequence of the magmatic domain that prevails along an accretionary boundary.