A new group contribution method for the estimation of properties of pure organic compounds is presented. Estimation is performed at two levels: the basic level uses contributions from first-order groups, while the next higher level uses a small set of second-order groups having the first-order groups as building blocks. Thus, the method provides both a first-order approximation (first-order group contributions) and a more accurate second-order prediction (first- and second-order group contributions). This article discusses methods for prediction of normal boiling point, normal melting point, critical pressure, critical temperature, critical volume, standard enthalpy of vaporization at 298 K, standard Gibbs energy, and standard enthalpy of formation at 298 K. The predictions are based exclusively on the molecular structure of the compound, and the method is able to distinguish among isomers. Compared to the currently-used methods, this technique demonstrates significant improvements in accuracy and applicability.