The invention provides a process to prepare very low sulphur, very low aromatic hydrocarbon fluids having a boiling range in the range of from 100 to 400° C. and a boiling range of not more than 80° C., comprising at least the two successive steps of —deep hydrodesulphurating of middle distillate down to less than 10 ppm sulphur, and —catalytic hydrogenating the desulphurized middle distillates of preceding step at a temperature from 80 to 180° C. and at a pressure from 60 to 160 bars.