Electron-nuclear double-resonance (ENDOR) measurements are performed in undoped, doped, and compensated a-Si:H. Matrix ENDOR and distant ENDOR are identified as the effective ENDOR mechanisms by an investigation of the transient ENDOR response, and conditions for the experimental parameters to optimize the response are given. ENDOR spectra due to $^{1}\mathrm{H}$ and $^{31}\mathrm{P}$ nuclei are found to be subject to a microwave coherence splitting, which allows a calibration of the microwave field in the ESR cavity. Several well-resolved lines of unknown origin are observed in compensated a-Si:H by light-induced ENDOR. It is shown that transient ENDOR experiments can be used to measure electronic and nuclear spin-lattice relaxation times at low temperatures and an application of this capability to study reversible light-induced changes in a-Si:H is presented. The discussion of the experimental results addresses the question of what kind of information about the structure of a-Si:H can be obtained by ENDOR experiments.