Madeira island consists of Miocene to Pleistocene lavas and pyroclasts. Major rock types are alkali-basalts, basanites and hawaiites; principal soil types are leptosols, andosols and cambisols. Our main objective was to link the chemistry of ground waters to weathering reactions and rates. We collected 40 shallow groundwater samples, remote from human activities. With a few exceptions, the ranges of electrical conductivities were 29 -176 mS/cm and of pH 5.8-8.5. The calculated P CO 2 was generally higher than the atmospheric value. The contribution of sea salt to the water chemistry was 30^9%. Corrected for sea salt, the cation concentrations (in meq/l) decrease in the order CaThe concentrations of SO 4 22 and NO 3 2 are very low. We calculated that the total annual chemical denudation rate in the studied area amounts to 37^12 g/m 2 , consuming 0.86^0.38 mol CO 2 /m 2 . To achieve our main objective, a set of mole balance equations-ðAX ¼ BÞ-was used, where A is a composite matrix of coefficients, including ratios between stoichiometric coefficients as determined by the weathering reactions and coefficients accounting for unconstrained contributions, B is the vector with a water composition, and X is the set of mole fractions of dissolved primary minerals plus the residual concentrations of the unconstrained contributions. Olivine (Ol), pyroxene (Py) and plagioclase (Pl) were considered to be the major primary minerals, and smectite, vermiculite, halloysite, allophane, gibbsite and hematite the secondary minerals in the weathering reactions. Using iterative procedures, whereby mixtures of secondary products as well as the composition of plagioclase are allowed to change, we selected one best-fit set of weathering reactions for each spring by checking all possible solutions of the mole balances against predefined boundary conditions. At odds with Goldich (1938) sequence, our model results indicate-for most best -fit sets-a weathering rate sequence of Pl . Ol . Py, but such reverse order is not unique. On average, the annual weathering rates (in mol/(ha y vol% mineral)) are 44^19 (Pl), 29^14 (Ol) and 22^13 (Py). q