The unified representation of spectral moments, classic topologic indices, quadratic indices, and stochastic molecular descriptors show that all these molecular descriptors lie within the same family. Consequently, the same prior probability for a successful quantitative-structure-activity-relationship (QSAR) may be expected irrespective of which indices are selected. Herein, we used stochastic spectral moments as molecular descriptors to seek a QSAR using a database of 221 bioactive compounds previously tested against diverse RNA-viruses and 402 nonactive ones. The QSAR model thus obtained correctly classifies 90.9% of compounds in training. The model also correctly classifies a total of 87.9% of 207 compounds on additional external predicting series, 73 of them having anti-RNA-virus activity and 134 nonactive ones. In addition, all compounds were regrouped into five different subsets for leave-group-out studies: (1) anti-influenza, (2) anti-picornavirus, (3) anti-paramyxovirus, (4) anti-RSV/anti-influenza, and (5) broad range anti-RNA-virus activity. The model has retained overall accuracies of about 90% on these studies validating model robustness. Finally, we exemplify the practical use of the model with the discovery of compounds 124 and 128. These compounds presented MIC50 values=3.2 and 8 microg/mL against respiratory syncytial virus (RSV) respectively. Both compounds also have low cytotoxicity expressed by their Minimal Cytotoxic Concentrations >400 microg/mL for HeLa cells. The present approach represents an effort toward a formalization and application of molecular indices in bioorganic and medicinal chemistry.