This paper presents a sleep stage recognition system for Awake, rapid eye movement (REM) and non-REM (NREM) sleep detection. Two respiratory variability (RV) features are extracted from oro-nasal airflow signals provided in the sleep-EDF (Expanded) database. A two layer system with threshold comparison classifier is implemented. This system achieved state-of-the-art performance with simple features and classifiers. The average accuracy of 74.00%±5.30% and Cohen's kappa coefficient of 0.49±0.08 were achieved with 21 recordings. In the end, the measure of sleep efficiency was calculated and the average absolute error was 3.61%±3.66%.