Olefins having from 2 to 8 carbon atoms are hydroformylated in a process in which (i) an olefin-containing feed in which a proportion of a saturated hydrocarbon having from 2 to 8 carbon atoms is present and also carbon monoxide and hydrogen are fed into a reaction zone and reacted in the presence of a hydroformylation catalyst, (ii) a stream consisting essentially of unreacted olefin and saturated hydrocarbon is separated off from the output from the reaction zone, (iii) the stream is separated into an olefin-enriched fraction and an olefin-depleted fraction by rectification, and (iv) at least part of the olefin-enriched fraction is recirculated to the reaction zone.