A process for hydroprocessing a hydrocarbon feedstock, includes the steps
of providing a hydrocarbon feed having an initial characteristic;
providing a first hydrogen-containing gas; feeding the hydrocarbon feed
and the first hydrogen-containing gas cocurrently to a first
hydroprocessing zone so as to provide a first hydrocarbon product;
providing a plurality of additional hydroprocessing zones including a
final zone and an upstream zone; feeding the first hydrocarbon product
cocurrently with a recycled gas to the upstream zone so as to provide an
intermediate hydrocarbon product; and feeding the intermediate
hydrocarbon product cocurrently with a second hydrogen-containing gas to
the final zone so as to provide a final hydrocarbon product having a
final characteristic which is improved as compared to the initial
characteristic.