Human sleep consists of wake, rapid-eye-movement (REM) sleep, and non-REM (NREM) sleep that includes light and deep sleep stages. This work investigated the time delay between changes of cardiac and brain activity for sleep transitions. Here, the brain activity was quantified by electroencephalographic (EEG) mean frequency and the cardiac parameters included heart rate, standard deviation of heartbeat intervals, and their low- and high-frequency spectral powers. Using a cross-correlation analysis, we found that the cardiac variations during wake-sleep and NREM sleep transitions preceded the EEG changes by 1-3 min but this was not the case for REM sleep transitions. These important findings can be further used to predict the onset and ending of some sleep stages in an early manner.