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Abstract Piton de la Fournaise (Réunion, Indian Ocean) is a large active volcano which shares many features with the Hawaiian volcanoes. Its particularly simple elemental and isotopic geochemistry suggests, however, a rather homogeneous mantle source and makes this volcano ideally suited for petrogenetic studies. We report mineralogical descriptions, major element, trace element and Sr isotope compositions of four volcanic sequences spanning the 530 ka of the known lifetime of the volcano. The lavas change with time from mildly alkalic to mildly tholeiitic. This change is due to crystal fractionation becoming shallower with time as olivine replaces clinopyroxene as the liquidus phase at lower pressure. Fractionation of an olivine–clinopyroxene assemblage at lithospheric-mantle pressure drives tholeiitic basalts into the field of alkali basalts and puts some limitation on trace-element modelling of the melting process. Most Fournaise lavas are basalts with a narrow compositional range (steady-state basalts) and picrites containing common plastically deformed phenocrysts. The buffering of the compatible element compositions indicates that the lavas last equilibrated in solid-dominant conditions which are incompatible with magma chamber processes and may have resulted from the ascent of liquid-rich zones through dykes filled with a slurry of olivine ± clinopyroxene crystals. A quantitative model describing mass balance during the displacement of a solitary porosity wave leaving behind cumulates with residual porosity accounts for the major and trace element distributions.The dykes are flushed during major magma surges forming picritic slurries (= oceanites). The transient alkalic lavas are products of dynamic crystallization on cold dyke walls during times of lower magma fluxes. The total lifetime of a Réunion volcano (≥ 2.1 my) includes early and waning stages with alkalic activity bracketing a steady-state stage of tholeiitic activity. We estimate that Réunion volcanism results from the impingement on the base of lithosphere of a solitary wave of hotspot material with a radius of 100–130 km and a velocity of 5–9 cm/yr.