Using quasielastic neutron scattering, we have investigated diffusion dynamics of protons in the protic ionic liquid, N,N,N',N'-tetramethylguanidinium bis(perfluoroethylsulfonyl)imide, a promising new compound for application as an electrolyte in proton-conducting fuel cells. A temperature range of 30-360 K has been studied. The melting temperature of N,N,N',N'-tetramethylguanidinium bis(perfluoroethylsulfonyl)imide is about 290 K. We have found four distinct dynamic processes. First, the methyl group rotations exhibit broadly distributed dynamics which, on the nanosecond time scale, become visible above approximately 100 K. Second, there is a localized process with a characteristic confinement radius of about 1.6 angstrom, which likely involves protons of the -NH2 groups. These two processes take place in both solid and liquid phases, even though the methyl group rotations in the liquid phase are likely too fast to be detected in our experiment. Above the melting temperature, there are two new diffusion processes contributing to the dynamics of the liquid phase. Both of them appear to be of translational character. However, only the slower process represents unrestricted translation diffusion. The faster process is better described as spatially restricted translational diffusion with a characteristic confinement radius of about 8 angstrom. It is likely that the long-range proton transfer in N,N,N',N'-tetramethylguanidinium bis(perfluoroethylsulfonyl)imide is associated primarily with the unrestricted translational diffusion process, which is characterized by a diffusion coefficient varying from 0.4 x 10(-10) to 1.4 x 10(-10) m(2)/s in the temperature range of 320-360 K.