This paper uses spectral analysis and correlation dimension index to examine the developmental differences between the EEG measured from two hippocampal subfields, CA1 and the dentate gyrus. The study was focused on the hippocampal EEG during the vigilance state of REM sleep in freely moving rats of 15 and 90 days of age. Power spectra, magnitude-squared coherence, and correlation dimension were estimated. The correlation dimension adds a new interpretation from the nonlinear dynamics perspective, and we found that there are no significant developmental differences between the granule cells of the dentate gyrus and the pyramidal cells of area CA1 when the theta activity was present during REM sleep.