This paper reports a preliminary investigation to evaluate the significance of various nonlinear dynamics approaches to analyze the heart rate variability (HRV) signal in children with sleep disordered breathing (SDB). Data collected from children in the age group of 1-17 years diagnosed with sleep apnea were used in this study. Both short term (5 minutes) and long term data from a full night polysomnography (7-9 hours) were analyzed. For short term data, the presence of nonstationarity in the derived HRV signal was determined by calculating the local Hurst exponent. Poincare plots and approximate entropy (ApEn) were then used to show the presence of correlation in the data. For long term data, the derived HRV signal was first separated into corresponding sleep stages with the aid of the recorded sleep hypnogram values at 30 seconds epochs. The scaling exponents using detrended fluctuation analysis (DFA) and the ApEn were then calculated for each sleep stage. Data from two sample subjects recorded for different sleep stages and breathing patterns were considered for short term analysis. Data from 7 sample subjects (after sleep staging) were considered for long term analysis. The accuracy rate of ApEn was about 72% for both long term and short term data sets. The accuracy rate of Alpha (alpha) derived from DFA for long term correlations was 57%. Further work is necessary to improve on the accuracies of these useful nonlinear dynamic measures and determine their sensitivity and specificity to detect SDB in children.