Polysomnography (PSG) is currently considered the gold standard for assessing sleep quality. However, the numerous sensors that must be attached to the subject can disturb sleep and limit monitoring to within hospitals and sleep clinics. If data could be obtained without such constraints, sleep monitoring would be more convenient and could be extended to ordinary homes. During rapid-eye-movement (REM) sleep, respiration rate and variability are known to be greater than in other sleep stages. Hence, we calculated the average rate and variability of respiration in an epoch (30 s) by applying appropriate smoothing algorithms. Increased and irregular respiratory patterns during REM sleep were extracted using adaptive and linear thresholds. When both parameters simultaneously showed higher values than the thresholds, the epochs were assumed to belong to REM sleep. Thermocouples and piezoelectric-type belts were used to acquire respiratory signals. Thirteen healthy adults and nine obstructive sleep apnea (OSA) patients participated in this study. Kappa statistics showed a substantial agreement (kappa > 0.60) between the standard and respiration-based methods. One-way ANOVA analysis showed no significant difference between the techniques for total REM sleep. This approach can also be applied to the non-intrusive measurement of respiration signals, making it possible to automatically detect REM sleep without disturbing the subject.