Process for continuous hydrogenation or hydrogenating amination

A process continuously hydrogenating unsaturated compounds, in which particles of a first hydrogenation catalyst are suspended in a liquid phase in which an unsaturated compound is dissolved, the liquid phase, in the presence of a hydrogenous gas at a first partial hydrogen pressure and at a first temperature, is conducted through a packed bubble column reactor in cocurrent counter to the direction of gravity, the effluent from the bubble column reactor is sent to a gas-liquid separation, the liquid phase is sent to a crossfiltration to obtain a retentate and a filtrate, the retentate is recycled into the bubble column reactor and the filtrate, in the presence of a hydrogenous gas at a second partial hydrogen pressure and at a second temperature, is passed over a bed of a second hydrogenation catalyst, the second partial hydrogen pressure is at least 10 bar higher than the first partial hydrogen pressure.