This paper presents a method for classifying wakefulness, REM, light and deep sleep based on the analysis of respiratory activity and body motions acquired by a bioradar. The method was validated using data of 32 subjects without sleep-disordered breathing, who underwent a polysomnography study in a sleep laboratory. We achieved Cohen's kappa of 0.49 in the wake-REM-light-deep sleep classification, 0.55 for the wake-REM-NREM classification and 0.57 for the sleep/wakefulness determination. The results might be useful for the development of unobtrusive sleep monitoring systems for diagnostics, prevention, and management of sleep disorders.