Process for preparing aldehydes by hydroformylation of olefins, wherein the process comprises the following steps: a) hydroformylating C4 to C20 olefins, preferably C8 to C12 olefins, in a reaction zone in the presence of synthesis gas and a homogeneous rhodium catalyst system at a pressure of 100 to 350 bar and a temperature of 90°C to 250°C to obtain a biphasic hydroformylation mixture, i.e. one comprising a gas phase and a liquid phase, containing at least unconverted olefins, synthesis gas, the homogeneous rhodium catalyst system and the aldehydes formed, and which is withdrawn from the at least one reaction zone; b) firstly expanding the hydroformylation mixture to a pressure between 11 bar and 50 bar, and separating the hydroformylation mixture into a first gaseous phase especially comprising the synthesis gas, and a first liquid phase especially comprising the unconverted olefins, the homogeneous rhodium catalyst system and the aldehydes formed; c) secondly expanding the first liquid phase obtained from step b) to a pressure between 10 mbar and 10 bar, and separating it into a second gaseous phase especially comprising the synthesis gas, and a second liquid phase especially comprising the unconverted olefins, the homogeneous rhodium catalyst system and the aldehydes formed; and d) feeding the second liquid phase to a removal, wherein, in a first step, a thermal separation is conducted in order to remove the aldehydes formed, and, in a second step, a preferably multistage membrane separation is conducted in order to remove the rhodium catalyst system, characterized in that the biphasic hydroformylation mixture prior to the first expansion in step b), the first liquid phase prior to the second expansion in step c), or the second liquid phase prior to the feeding to a removal in step d) is cooled to a temperature between 40 and 100°C, preferably between 50 and 95°C, more preferably between 60 and 90°C. a) hydroformylating C4 to C20 olefins, preferably C8 to C12 olefins, in a reaction zone in the presence of synthesis gas and a homogeneous rhodium catalyst system at a pressure of 100 to 350 bar and a temperature of 90°C to 250°C to obtain a biphasic hydroformylation mixture, i.e. one comprising a gas phase and a liquid phase, containing at least unconverted olefins, synthesis gas, the homogeneous rhodium catalyst system and the aldehydes formed, and which is withdrawn from the at least one reaction zone; b) firstly expanding the hydroformylation mixture to a pressure between 11 bar and 50 bar, and separating the hydroformylation mixture into a first gaseous phase especially comprising the synthesis gas, and a first liquid phase especially comprising the unconverted olefins, the homogeneous rhodium catalyst system and the aldehydes formed; c) secondly expanding the first liquid phase obtained from step b) to a pressure between 10 mbar and 10 bar, and separating it into a second gaseous phase especially comprising the synthesis gas, and a second liquid phase especially comprising the unconverted olefins, the homogeneous rhodium catalyst system and the aldehydes formed; and d) feeding the second liquid phase to a removal, wherein, in a first step, a thermal separation is conducted in order to remove the aldehydes formed, and, in a second step, a preferably multistage membrane separation is conducted in order to remove the rhodium catalyst system,