The dynamic relaxation properties of amorphous rubbery networks prepared by the UV photopolymerization of poly(ethylene glycol) diacrylate [PEGDA] and poly(propylene glycol) diacrylate [PPGDA] cross-linkers have been investigated using broadband dielectric spectroscopy. Effective cross-link density in the networks was controlled by copolymerization of the diacrylate cross-linkers with monofunctional acrylates of similar chemical composition. For all of the networks examined, three motional transitions were detected with increasing temperature, including an intermediate "fast" relaxation located between the typical sub-glass and glass-rubber processes and corresponding to a subset of constrained segmental motions that were more local and less cooperative in nature as compared to those associated with the glass transition. The properties of the intermediate relaxation were sensitive to the degree of constraint imposed by the cross-link junctions: the dielectric intensity of the fast process decreased with decreasing effective cross-link density, and the characteristic relaxation broadening associated with this transition was less pronounced in networks containing a lower degree of cross-linking. The intermediate process detected in the cross-linked networks was comparable to a distinct sub-glass dispersion measured in crystalline poly(ethylene oxide) [PEO] and which has been attributed to constrained motions originating in the vicinity of the crystal-amorphous interface.