The transformation of dibenzothiophene and 4,6-dimethyldibenzothiophene was carried out in a flow reactor at 340 degrees C under a 3.0 MPa hydrogen pressure. A sulfided NiMo on alumina was used as reference catalyst. The effect of the acidity was studied by mixing this catalyst with silica-alumina, or by using a bifunctional NiMo-Y zeolite catalyst. On the sulfided NiMo on alumina catalyst, dibenzothiophene transformed mainly through direct desulfurization, yielding biphenyl. This reaction was much slower in the case of 4,6-dimethyldibenzothiophene, which renders the molecule less reactive. The addition of an acidic function to the sulfide catalyst did not modify the reactivity of dibenzothiophene while it strongly increased that of 4,6-dimethyldibenzothiophene. This is attributed to the isomerization of 4,6-dimethyldibenzothiophene into 3,6-dimethyldibenzothiophene, which is more reactive than 4,6-dimethyldibenzothiophene. In the presence of an acidic component, cracking of the desulfurized molecules can also be observed.