Process and apparatus for desulfurizing the gaseous product of the vacuum distillation of the heavy fraction of crude oil. The initial gaseous mixture (8) to be desulfurized is an incondensible gas that contains hydrogen sulfide. A gas-liquid contact column (2) contains first and second sections (3, 4) that contain beds of packing material, which may be structured or random packing. The beds are supported below irrigation devices (18) that promote the wetting of the beds but cause minimal pressure loss in the gases passing through the column. The initial gaseous mixture is dried and introduced (14) into the first section (3) of the column. Also introduced into the first section of the column is a fresh ammonia solution (9) containing the stoichiometric quantity for reacting with the amount of hydrogen sulfide present in the initial gaseous mixture. Finally, the first section of the column receives a second ammonia solution that is passed from the second section of the column into the first section.