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 1H spin-lattice relaxation rate, R1, 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 a modified Stokes-Einstein diffusion/viscosity relation. The main difference between the relaxation mechanisms responsible for R1 in the two IL systems is related to the additional paramagnetic relaxation contribution associated with the 1H spins-[FeCl4] paramagnetic moments' interactions. Cross-relaxation cusps in the R1 dispersion, associated with 35Cl and 1H nuclear spins in the IL systems, were detected. The R1 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.