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This paper describes a noninvasive algorithm to estimate the sleep stages used in the Rechtschaffen and Kales method (R-K method). The heartbeat and body-movement signals measured by the noninvasive pneumatic method are used to estimate the sleep stages instead of using the Eletroencephalogram and Electromyography in the R-K method. From the noninvasive measurements, we defined two indices that indicate the condition of REM sleep and the sleep depth. Functions to obtain the incidence ratio and the standard deviation of the extracted elements for each sleep stage were also determined, for each age group of the subjects. Using these indices and functions, an algorithm to classify the subjects' sleep stages was proposed. The mean agreement ratios between the sleep stages' data obtained from the proposed method and those from the de facto standard R-K method, for the stages categorized into six, five, and three, were 51.6%, 56.2%, and 77.5%, and their corresponding mean values of kappa statistics were 0.29, 0.39, and 0.48, respectively. The proposed method shows closer agreement with the result of R-K method than the similar noninvasive method presented earlier.