We present a computational study of the structure and of the transport properties of electrolytes based on Li[(CF3SO2)2N] solutions in mixtures of sulfoxides and sulfones solvents. The simulations of the liquid phases have been carried out using molecular dynamics with a suitably parametrized model of the intermolecular potential based on a polarizable expression of the electrostatic interactions. Pulse field gradient NMR measurements have been used to validate and support the computational findings. Our study show that the electrolytes are characterized by extensive aggregation phenomena of the support salt that, in turn, determine their performance as conductive mediums.