Obstructive sleep apnea syndrome (OSAS) is observed in approximately 2% of children. Heart rate variability (HRV) is a potentially simple, non-invasive diagnostic screening tool for OSAS. In this study, we investigated the diagnostic potential of HRV using power spectral analysis, numerical titration, sample entropy, and detrended fluctuation analysis. Effects of sleep stages (REM and NREM sleep) are evaluated. The results show that the heart rate chaos intensity, as measured by the noise limit in numerical titration, is significantly higher during REM sleep than NREM sleep in all patient groups. By using the receiver-operating characteristic analysis, the detection of OSAS yielded a specificity of 72.2% and sensitivity of 81.3% using the numerical-titration technique. The findings suggest that sleep state and disordered breathing are important determinants of cardiac autonomic control. Nonlinear techniques such as numerical titration, when used in conjunction with spectral analysis of HRV could be an effective screening tool for pediatric OSAS.