Methods of computer-assisted diagnostics that utilize deep learning techniques on recordings of respiratory sounds have been developed to diagnose bronchial asthma. In the course of the study an anonymous database containing audio files of respiratory sound recordings of patients suffering from different respiratory diseases and healthy volunteers has been accumulated and used to train the software and control its operation. The database consists of 1,238 records of respiratory sounds of patients and 133 records of volunteers. The age of tested persons was from 18 months to 47 years. The sound recordings were captured during calm breathing at four points: in the oral cavity, above the trachea, at the chest, the second intercostal space on the right side, and at the point on the back. The developed software provides binary classifications (diagnostics) of the type: “sick/healthy” and “asthmatic patient/non-asthmatic patient and healthy”. For small test samples of 50 (control group) to 50 records (comparison group), the diagnostic sensitivity metric of the first classifier was 88%, its specificity metric –86% and accuracy metric –87%. The metrics for the classifier “asthmatic patient/non-asthmatic patient and healthy” were 92%, 82%, and 87%, respectively. The last model applied to analyze 941 records in asthmatic patients indicated the correct asthma diagnosis in 93% of cases. The proposed method is distinguished by the fact that the trained model enables diagnostics of bronchial asthma (including differential diagnostics) with high accuracy irrespective of the patient gender and age, stage of the disease, as well as the point of sound recording. The proposed method can be used as an additional screening method for preclinical bronchial asthma diagnostics and serve as a basis for developing methods of computer assisted patient condition monitoring including remote monitoring and real-time estimation of treatment effectiveness.