The phase relationships of three peralkaline rhyolites from the Kenya Rift have been established at 150 and 50 MPa, at oxygen fugacities of NNO - 1·6 and NNO + 3·6 (log fO2 relative to the Ni–NiO solid buffer), between 800 and 660°C and for melt H2O contents ranging between saturation and nominally anhydrous. The stability fields of fayalite, sodic amphiboles, chevkinite and fluorite in natural hydrous silicic magmas are established. Additional phases include quartz, alkali feldspar, ferrohedenbergite, biotite, aegirine, titanite, montdorite and oxides. Ferrohedenbergite crystallization is restricted to the least peralkaline rock, together with fayalite; it is replaced at low melt water contents by ferrorichterite. Riebeckite–arfvedsonite appears only in the more peralkaline rocks, at temperatures below 750°C (dry) and below 670°C at H2O saturation. Under oxidizing conditions, it breaks down to aegirine. In the more peralkaline rocks, biotite is restricted to temperatures below 700°C and conditions close to H2O saturation. At 50 MPa, the tectosilicate liquidus temperatures are raised by 50–60°C, and that of amphibole by 30°C. Riebeckite–arfvedsonite stability extends down nearly to atmospheric pressure, as a result of its F-rich character. The solidi of all three rocks are depressed by 40–100°C compared with the solidus of the metaluminous granite system, as a result of the abundance of F and Cl. Low fO2 lowers solidus temperatures by at least 30°C. Comparison with studies of metaluminous and peraluminous felsic magmas shows that plagioclase crystallization is suppressed as soon as the melt becomes peralkaline, whatever its CaO or volatile contents. In contrast, at 100 MPa and H2O saturation, the liquidus temperatures of quartz and alkali feldspar are not significantly affected by changes in rock peralkalinity, showing that the incorporation of water in peralkaline melts diminishes the depression of liquidus temperatures in dry peralkaline silicic melts compared with dry metaluminous or peraluminous varieties. At 150 MPa, pre-eruptive melt H2O contents range from 4 wt % in the least peralkaline rock to nearly 6 wt % in the two more peralkaline compositions, in broad agreement with previous melt inclusion data. The experimental results imply magmatic fO2 at or below the fayalite–quartz–magnetite solid buffer, temperatures between 740 and 660°C, and melt evolution under near H2O saturation conditions.