Structure-activity relationships (SAR) are studied in the series of 4,4- disubstituted piperidine morphinomimetics (42 compounds) by means of the Electronic-Topological Method (ETM). In the frameworks of this approach, its input data were taken as the results of conformational and quantum-mechanical calculations. These calculations had been carried out for all compounds from the series under study, taking into account their neutral and protonated by the nitrogen of piperidine cycle forms. The ETM application resulted in a set of pharmacophores and anti-pharmacophores, which formed a basis of a system used to predict analgesic activity. First of all, the system was tested on known analgesics. Testing has shown a good agreement with the experimental data. Then, the system was applied to a few compounds with similar structures but unknown activity. The results of the study could be used for computer screening and design of novel compounds with analgesics properties as new potential drugs.