The invention relates to processes for preparing aldehydes by hydroformylation of alkenes, in which an alkene-containing feed mixture is subjected to a primary hydroformylation with synthesis gas in the presence of a homogeneous catalyst system, the primary hydroformylation being effected in a primary reaction zone from which a cycle gas containing at least some of the products and unconverted reactants of the primary hydroformylation are drawn off continuously and partly condensed, with recycling of uncondensed components of the cycle gas into the primary reaction zone, and with distillative separation of condensed components of the cycle gas in an aldehyde removal stage to give an aldehyde-rich mixture and a low-aldehyde mixture. The problem that it addresses is that of developing the process such that it achieves high conversions and affords aldehyde in good product quality even in the case of a deteriorating raw material position. More particularly, a solution is to be found for making legacy oxo process plants capable of utilizing lower-value raw material sources. This problem is solved by separating the low-aldehyde mixture into a retentate and a permeate by means of a membrane separation unit in such a way that alkenes present in the low-aldehyde mixture become enriched in the permeate, while alkanes present in the low-aldehyde mixture become enriched in the retentate. The alkene-rich permeate is then transferred into a secondary reaction zone and subjected to a secondary hydroformylation therein with synthesis gas in the presence of an SILP catalyst system. The reaction product obtained from the secondary hydroformylation is recycled into the aldehyde removal stage.