The invention concerns a process for improving the pour point of a feed comprising paraffins containing more than 10 carbon atoms, in which process the feed to be treated is brought into contact with a catalyst comprising an NU-87 zeolite comprising silicon and at least one clement T selected from the group formed by Al, Fe, Ga and B, from which at least a portion of clement T has been removed, and having a global Si/T ratio of over 20, the catalyst also containing at least one hydro-dehydrogenating element. The process is carried out at a temperature which is in the range 170.degree. C. to 500.degree. C., a pressure in the range 1 to 250 bar and at an hourly space velocity in the range 0.05 to 100 h.sup.-1, in the presence of hydrogen in a proportion of 50 to 2000 l/l of feed. The oils obtained have good pour points and high viscosity indices (VI). The process is also applicable to gas oils and other feeds requiring a reduction of pour point. The catalyst is also claimed.