The invention concerns a fixed bed process for capturing arsenic and for desulphurizing a hydrocarbon fraction comprising olefins, sulphur and arsenic, said process comprising a step a) for bringing a capture mass into contact with said hydrocarbon fraction in the presence of hydrogen, the ratio between the flow rate of hydrogen and the flow rate of the hydrocarbon fraction being in the range 50 to 800 Nm3/m3, the operating temperature being in the range 200° C. to 400° C., the operating pressure being in the range 0.2 to 5 MPa. The capture mass comprises molybdenum in a sulphurized form, nickel in a sulphurized form and at least one porous support selected from the group constituted by aluminas, silica, silica-aluminas, titanium oxide and magnesium oxide. The nickel content is in the range 10% to 28% by weight and the molybdenum content is in the range 0.3% to 2.1% by weight.