The ONCONET telemedicine system, intended for remote monitoring of the health status of cancer patients, is presented. The interactive part in asynchronous mode provides virtual contacts in form of medical records: patient’s questions, doctor’s answers, questionnaires filled up by patients. On-line video conversations are possible in emergency. The patient can add any medical documents in his health monitoring record. The analytical subsystem, using artificial intelligence elements, reveals signs of alarm situations in patient messages automatically. The subsystem estimates necessity to demand attention of the doctor or emergency services. Special questionnaires devoted to COVID-19 had been developed. All the data can be represented in integrated form on common-time scale graphs and colored diagrams (“heat maps”) reflecting health statement of a patient. There are video teaching cases and medical information materials particularly connected to COVID-19. The System collects, organizes and saves personal medical information according with personal electronic medical case history structure. The system had been tested in 22 medical organizations in Russia. Ways of further perspective research and development of the system are discussed.