A study is presented of the molecular dynamics and of the viscosity in pure [Aliquat][Cl] ionic liquid and in a mixture of [Aliquat][Cl] with 1% (v/v) of [Aliquat][FeCl4]. The H-1 spin-lattice relaxation rate, RI, was measured by NMR relaxometry between 8 and 300 MHz. In addition, the translation self-diffusion, D, was measured by pulse field gradient NMR. The ILs' viscosity was measured as a function of an applied magnetic field, B; and it was found that the IL mixture's viscosity decreased with increasing B, whereas the [Aliquat] [Cl] viscosity is independent of B. All experimental results were analyzed taking into account the viscosity's magnetic field dependence, assuming modified Stokes-Einstein diffusion/viscosity relation. The main difference between the relaxation mechanisms responsible for R-1 in the two IL systems is related to the additional paramagnetic relaxation contribution associated with the H-1 spins-[FeCl4] paramagnetic moments' interactions. Cross-relaxation cusps in the R-1 dispersion, associated with Cl-35 and H-1 nuclear spins in the IL systems, were detected. The R-1 model considered was successfully fitted to the experimental results, and it was possible to estimate the value of D at zero field in the case of the IL mixture which was consistent with the values of D measured at 7 and 14.1 T and with the magnetic field dependence estimated from the viscosity measurements. It was observed that a small concentration of [Aliquat][FeCl4] in the [Aliquat][Cl] was enough to produce a "superparamagnetic"-like effect and to change the IL mixture's molecular dynamics and viscosity and to allow for their control with an external magnetic field.