A proton nuclear magnetic relaxation dispersion (1)H NMRD study of the molecular dynamics in mixtures of magnetic ionic liquid [P66614][FeCl4] with [P66614][Cl] ionic liquid and mixtures of [P66614][FeCl4] with dimethyl sulfoxide (DMSO) is presented. The proton spin-lattice relaxation rate, R1, was measured in the frequency range of 8 kHz-300 MHz. The viscosity of the binary mixtures was measured as a function of an applied magnetic field, B, in the range of 0-2 T. In the case of DMSO/[P66614][FeCl4] the viscosity was found to be independent from the magnetic field, while in the case of the [P66614][Cl]/[P66614][FeCl4] system viscosity decreased with the increase of the magnetic field strength. The spin-lattice relaxation results were analyzed for all systems taking into account the relaxation mechanisms associated with the molecular motions with correlation times in a range between 10(-11) and 10(-7)s, usually observed by NMRD, and the paramagnetic relaxation contributions associated with the presence of the magnetic ions in the systems. In the case of the DMSO/[P66614][FeCl4] system the R1 dispersion shows the relaxation enhancement due to the presence of the magnetic ions, similar to that reported for contrast agents. For the [P66614][Cl]/[P66614][FeCl4] system, the R1 dispersion presents a much larger paramagnetic relaxation contribution, in comparison with that observed for the DMSO/[P66614][FeCl4] mixtures but different from that reported for other magnetic ionic liquid system. In the [P66614][Cl]/[P66614][FeCl4] system the relaxation enhancement associated with the paramagnetic ions is clearly not proportional to the concentration of magnetic ions, in contrast with what is observed for the DMSO/[P66614][FeCl4] system.