The invention relates to a method for the continuous production of aldehydes comprising between 5 and 21 carbon atoms, by the isomerising hydroformylation in a homogenous phase of olefin compositions comprising between 4 and 20 carbon atoms and containing α-olefins and olefins with internal double bonds, by means of a synthesis gas, in the presence of a homogeneous rhodium catalyst that is complexed with an organophosphorus ligand containing oxygen atoms and/or nitrogen atoms and a free ligand. Said production is carried out at high temperature and high pressure in a multi-stage reaction system consisting of at least two reaction zones. According to said method, the olefin composition is first reacted in a first reaction zone or a group of several first reaction zones at a total pressure of between 10 and 40 bar, using a synthesis gas with a CO/H2 molar ratio of between 4:1 and 1:2 until a 40 to 95% conversion of the α-olefins is obtained. The hydroformylation product from the first reaction zone or group of several first reaction zones is then reacted in a subsequent reaction zone or group of several reaction zones at a total pressure of between 5 and 30 bar, using a synthesis gas with a CO/H2 molar ratio of between 1:4 and 1:1000. The total pressure in the subsequent reaction zone or zones is respectively 1 to (G1−Gf) bar lower than that of the preceding reaction zone, whereby G1 represents the total pressure in the respective preceding reaction zone and Gf represents the total pressure in the respective reaction zone that succeeds said first reaction zone or zones, with the proviso that the difference between G1 and Gf is greater than 1 bar and the partial CO pressure in the subsequent reaction zone or zones is respectively lower than that of the preceding reaction zone.