Strongly undersaturated rocks of the McMurdo Volcanic Group of late Cenozoic age at Brown Peninsula form three eruptive cycles of basaltic to salic lavas. Two cycles at Rainbow Ridge show a basanite to nepheline-hawaiite to nepheline-benmoreite and a basanite to nepheline-benmoreite eruptive sequence. Fractional crystallization processes for the sequence have been modeled using major-element least squares mass-balance models. Two models can explain the basanite to nepheline-hawaiite transition. Model 1 involves fractionation of olivine, clinopyroxene, plagioclase, opaque oxides, and apatite; model 2 is similar, but also includes kaersutite. The nepheline-hawaiite to nepheline-benmoreite transition involves fractionation of clinopyroxene, kaersutite, plagioclase, opaque oxides, and apatite. Trace-element (including rare-earth element) contents calculated using solutions from the mass-balance models are compatible with both models for the formation of nepheline-hawaiite. Excellent agreement is shown between calculated and observed trace-element data for the nepheline-benmoreite. Small pods of basanite, derived from a garnet peridotite mantle by a low degree of partial melting, have been intruded into the crust where subsequent fractional crystallization formed the intermediate and salic rocks. This process has apparently occurred repeatedly at many eruptive centers in the McMurdo Sound area.