Calculation of mineral and fluid volumetric concentrations from well logs is one of the most important outcomes of formation evaluation. Conventional estimation methods assume linear or quasi-linear relationships between volumetric concentrations of solid/fluid constituents and well logs. Experience shows, however, that the relationship between neutron porosity logs and mineral concentrations is generally nonlinear. More importantly, linear estimation methods do not explicitly account for shoulder-bed and/or invasion effects on well logs, nor do they account for differences in the volume of investigation of the measurements involved in the estimation. The latter deficiencies of linear estimation methods can cause appreciable errors in the calculation of porosity and hydrocarbon pore volume. We investigated three nonlinear inversion methods for assessment of volumetric concentrations of mineral and fluid constituents of rocks from multiple well logs. All three of these methods accounted for the general nonlinear relationship between well logs, mineral concentrations, and fluid saturations. The first method accounted for the combined effects of invasion and shoulder beds on well logs. The second method also accounted for shoulder-bed effects but was intended for cases where mud-filtrate invasion is negligible or radially deep. Finally, the third method was designed specifically for analysis of thick beds where mud-filtrate invasion is either negligible or radially deep. Numerical synthetic examples of application indicated that nonlinear inversion of multiple well logs is a reliable method to quantify complex mineral and fluid compositions in the presence of thin beds and invasion. Comparison of results against those obtained with conventional multimineral estimation methods confirmed the advantage of nonlinear inversion of multiple well logs in quantifying thinly bedded invaded formations with variable and complex lithology, such as those often encountered in carbonate formations.