A process for hydroformylating olefinically unsaturated compounds by means of a cobalt-based catalyst is carried out in a non-aqueous ionic liquid which is a liquid at a temperature below 90.degree. C. and comprises at least one ammonium and/or phosphonium and/or sulfonium cation Q.sup.+ and at least one anion A.sup.-; catalyst recycling is improved by using a ligand selected from the group consisting of Lewis bases and employing a depressurization step between the pressurized reaction step and the step for separating the phases by decanting. At the end of said depressurization step, the organic phase is separated in the decanting step and the non-aqueous ionic liquid containing the catalyst can be re-used.