Novel non-invasive methods for the diagnosis of malignancies should be effective for early diagnosis, reproducible, inexpensive, and independent from the human factor. Our aim was to establish the applicability of the non-invasive method, based on the analysis of air exhaled by patients who are at different stages of oropharyngeal, larynx and lung cancer. The diagnostic device includes semiconductor sensors capable of measuring the concentrations of gas components in exhaled air, with the high sensitivity of 1 ppm. The neural network uses signals from these sensors to perform classification and identify cancer patients. Prior to the diagnostic procedure of the non-invasive method, we clarified the extent and stage of the tumor according to current international standards and recommendations for the diagnosis of malignancies. The statistical dataset for neural network training and method validation included samples from 121 patients with the most common tumor localizations (lungs, oropharyngeal region and larynx). The largest number of cases (21 patients) were lung cancer, while the number of patients with oropharyngeal or laryngeal cancer varied from 1 to 9, depending on tumor localization (oropharyngeal, tongue, oral cavity, larynx and mucosa of the lower jaw). In the case of lung cancer, the parameters of the diagnostic device are determined as follows: sensitivity-95.24%, specificity-76.19%. For oropharyngeal cancer and laryngeal cancer, these parameters were 67.74% and 87.1%, respectively. This non-invasive method could lead to relevant medicinal findings and provide an opportunity for clinical utility and patient benefit upon early diagnosis of malignancies.