Resting state functional connectivity studies in fMRI have been used to demonstrate that the human brain is organized into inherent functional networks in the absence of stimuli. The basis for this activity is based on the spontaneous fluctuations observed during rest. In the present study, the time series generated from these fluctuations were characterized as either being linear or nonlinear based on the Delay Vector Variance method, applied through an examination of the local predictability of the signal. It was found that the default mode resting state network is composed of relatively more linear signals compared to the visual, task positive visuospatial, motor, and auditory resting state network time series. Also, it was shown that the visual cortex resting state network is more nonlinear relative to these aforementioned networks. Furthermore, using a histogram map of the nonlinearly characterized voxels for all the subjects, the histogram map was able to retrieve the peak intensity in four out of six resting state networks. Thus, the findings may provide the basis for a novel way to explore spontaneous fluctuations in the resting state brain.