Nematic liquid- crystal (LC) elastomers and gels have a rubbery polymer network coupled to the nematic director. While LC elastomers show a single, non- hydrodynamic relaxation mode, dynamic light- scattering studies of self- assembled liquid- crystal gels reveal orientational fluctuations that relax over a broad time scale. At short times, the relaxation dynamics exhibit hydrodynamic behavior. In contrast, the relaxation dynamics at long times are non-hydrodynamic, highly anisotropic, and increase in amplitude at small scattering angles. We argue that the slower dynamics arise from coupling between the director and the physically associated network, which prevents director orientational fluctuations from decaying completely at short times. At long enough times the network restructures, allowing the orientational fluctuations to fully decay. Director dynamics in the self- assembled gels are thus quite distinct from those observed in LC elastomers in two respects: they display soft orientational fluctuations at short times, and they exhibit at least two qualitatively distinct relaxation processes.