Abstract: The unify representation of spectral moments, classic topologic indices, quadratic indices, and stochastic molecular descriptors shown that all these molecular descriptors lie within the same family. Consequently, the same priori probability for a success quantitative-structure-activity-relationship (QSAR) may be expected no matter 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 non-active 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 non-active ones. In addition, all compounds were regrouped into five different subsets for leave-group-out studies: 1) antiinfluenza, 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 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 µg/mL against respiratory syncytial virus (RSV) respectively. Both compounds have also low cytotoxicity expressed by their Minimal Cytotoxic Concetrations > 400 µg/mL for HeLa cells. The present approach represent and effort toward a formalization and application of molecular indices in bioinformatics, bioorganic and medicinal chemistry.