Phase equilibrium experiments were performed on typical 'oceanic' and 'cratonic' peridotite compositions and a Ca, Al-rich orthopyroxene composition, to test the proposal that garnet lherzolites exsolved from high-temperature harzburgites, and to further our understanding of the origin of ancient cratonic lithospheres. 'Oceanic' peridotites crystallize a garnet harzburgite assemblage at pressures above 5 GPa in the temperature range 150-1600-degrees-C, but at 5 GPa and temperatures less than 1450-degrees-C, crystallize clinopyroxene to become true lherzolites. 'Cratonic' peridotites crystallize a garnet harzburgite assemblage at pressures above 5 GPa in the temperature range 1300-1600-degrees-C. Garnet-free harzburgite crystallizes from both 'cratonic' and 'oceanic' peridotite at temperatures above 1450-degrees-C and pressures below 4.5-5 GPa. Phase relations for the high Ca, Al-rich orthopyroxene composition essentially mirror those for 'oceanic' peridotite. The complete solution of garnet and clinopyroxene into orthopyroxene observed in all three starting compositions at temperatures near or above the mantle solidus at pressures less than 6 GPa supports the hypothesis that garnet lherzolite could have exsolved from harzburgite. The inferred cooling path for the original high-temperature harzburgite protoliths of garnet lherzolites differs depending on bulk composition. The precursor harzburgite protoliths of garnet lherzolites and harzburgites with 'cratonic' bulk compositions apparently experienced simple isobaric cooling from formation temperatures near the peridotite solidus to those at which most of these periodotites were sampled in the mantle (< 1200-degrees-C). The cooling histories for harzburgite protoliths of sheared garnet lherzolites with 'oceanic' compositional affinity are speculated to have involved convective circulation of mantle material to depths deeper than those at which it was originally formed. Phase equilibria and compositional relationships for orthopyroxenes produced in phase equilibrium experiments on peridotite and komatiite are consistent with an origin for 'cratonic' peridotite as a residue of Archean komatiite extraction, which has since cooled and exsolved clinopyroxene and garnet to become the common low-temperature, coarse-grained periodotite thought to comprise the bulk of the mantle lithosphere beneath the Archean Kaapvaal craton.