We examine the coherence in the spontaneous brain activity of sleeping children as measured by the blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) signals. The results are described in terms of resting-state networks (RSN) and their properties. More specifically, in this study we examine the effect of severe prematurity on the spatial location of the visual, temporal, motor, basal ganglia, and the default mode networks, the temporal response properties of each of these networks, and the functional connectivity between them. Our results suggest that the anatomical locations of the RSNs are well developed by 18 months of age and their spatial locations are not distinguishable between premature and term born infants at 18 months or at 36 months, with the exception of small spatial differences noted in the basal ganglia area and the visual cortex. The two major differences between term and pre-term children were present at 36 but not 18 months and include: (1) increased spectral energy in the low frequency range (0.01-0.06 Hz) for pre-term children in the basal ganglia component, and (2) stronger connectivity between RSNs in term children. We speculate that children born very prematurely are vulnerable to injury resulting in weaker connectivity between resting-state networks by 36 months of age. Further work is required to determine whether this could be a clinically useful tool to identify children at risk of developmental delay related to premature birth.