PURPOSE: To execute dewaxing with the formation of gaseous products suppressed by bringing a wax-contg. hydrocarbon oil to contact with a specified gallium silicate-contg. catalyst in the presence of hydrogen at a high temp. under high pressure.

CONSTITUTION: (i) Crystalline gallium silicate having a compsn. in which the molar ratio of the oxides, i.e., SiO2, to Ga2O3 is regulated to 100 to 500, preferably 110 to 350 and showing an X-ray diffraction pattern containing the four strongest lines at interplanar spacings of 11.1±0.2 , 10.0±0.2 , 3.84±0.07 and 3.72±0.06 is blended with (ii) a (de) hydrogenated metal selected from the group 2b, 4b, 5b, 6b, 7b and 8 metals (such as Pd) in the Periodic Table according to necessary to obtain a catalyst (B). (A) A wax-contg. hydrocarbon oil (such as a lubricating-base oil) is brought into contact with the B component in the presence of hydrogen of 5 to 100 bar at 200 to 500°C under the conditions in which the space velocity is regulated to 0.1 to 5 kg for the B component 1 l per hour and the ratio of hydrogen/the oil is regulated to 100 to 2500 Nl/Kg.