The Ideal Adsorbed Solution Theory (IAST) developed by Myers and Prausnitz and Radke and Prausnitz provides a powerful tool to calculate multicomponent adsorption equilibria based on single component adsorption isotherms. An important aspect of the application of IAST is that it requires the solution of an implicit algebraic system of equations. Analytical solutions can be derived only for few simple single component isotherm models. This work offers a new concept to solve the equations of the IAST for mixtures of N components characterized by nondecreasing single component adsorption isotherm behavior. The approach is based on transforming the algebraic system of IAST equations to a system of ODEs with one specified initial value. This work also provides analytical expressions for the partial derivatives of the predicted adsorption equilibria and increases the efficiency of numerical calculations for fixed-bed adsorber dynamics. The strength of the solution method is illustrated in case studies. (C) 2012 American Institute of Chemical Engineers AIChE J, 59: 1263-1277, 2013