In the existing quantitative structure-activity relationship (QSAR) methods any molecule is represented as a single point in a many-dimensional space of molecular descriptors. We propose a new QSAR approach based on Quantitative Neighbourhoods of Atoms (QNA) descriptors, which characterize each atom of a molecule and depend on the whole molecule structure. In the 'Star Track' methodology any molecule is represented as a set of points in a two-dimensional space of QNA descriptors. With our new method the estimate of the target property of a chemical compound is calculated as the average value of the function of QNA descriptors in the points of the atoms of a molecule in QNA descriptor space. Substantially, we propose the use of only two descriptors rather than more than 3000 molecular descriptors that apply in the QSAR method. On the basis of this approach we have developed the computer program GUSAR and compared it with several widely used QSAR methods including CoMFA, CoMSIA, Golpe/GRID, HQSAR and others, using ten data sets representing various chemical series and diverse types of biological activity. We show that in the majority of cases the accuracy and predictivity of GUSAR models appears to be better than those for the reference QSAR methods. High predictive ability and robustness of GUSAR are also shown in the leave-20%-out cross-validation procedure.