The invention relates to a process for improving the pour point of a feedstock that comprises paraffins of more than 10 carbon atoms, in which the feedstock that is to be treated is brought into contact with a catalyst that comprises the IM-5 zeolite and at least one hydro-dehydrogenating element, at a temperature of between 170 and 500.degree. C., a pressure of between 1 and 250 bar, and an hourly volume velocity of between 0.05 and 100 h.sup.-1, in the presence of hydrogen at a ratio of 50 to 2000 l/l of feedstock. The oils that are obtained have good pour points and high viscosity indices (VI). The process can also be applied to gas-oils and other feedstocks whose pour points need to be lowered.