Coumarin and its derivatives are reactive compounds, suitable for many syntheses. They are used as anticoagulants, antibacterial, animistic compounds. The interest in coumarins has increased because it was found that they reduce the HIV virus activity. The synthesis of 4-arylaminocoumarin derivatives from 4-hydroxycoumarin, has been carried out, and their antimycotic effects were tested. In the QSAR (quantitative structure-activity relationship) QSPR (quantitativestructure-property-activity relationship) study we have used physicochemical properties and topological indices (Balaban index J(G), Wiener index W(G), information-theoretical index I(G), and valence connectivity index (G), to predict bioactivity of the newly synthesized coumarin compounds. By using methods of molecular modelling, the relationships between structure, properties and activity of coumarin compounds have been investigated. The best QSPR models were obtained using valence connectivity index or combination indices. According Rekker's method the best correlation of calculated values log P, has been obtained with the model based on the inhibition zone (I) 4-arylaminocoumarin derivatives expressed in mm. The results obtained in this study enable further synthesis of new coumarin derivatives and predict their biological activity and properties.