A multistage process for the continuous expoxidation of double bonds of an unsaturated oily compound selected from the group consisting of terminal and non-terminal olefins having more than 12 carbon atoms, unsaturated higher fatty acids and their esters with lower alkanols and lower alkanediols, unsaturated aliphatic hydrocarbon alcohols having from 8 to 18 carbon atoms and triglycerides of higher fatty acids including unsaturated higher fatty acids using performic acid formed in situ from hydrogen peroxide and formic acid in an aqueous media consisting essentially of passing the reactants, the unsaturated oily compound pound and the hydrogen peroxide/formic acid aqueous phase under ambient pressure in cross-counter flow through an at least three-stage reaction cascade from stage 1 to stage n, of which the individual stages each consist of a stirrer-equipped reaction vessel and a phase separator, the dily phase being introduced into the first reaction stage, the concentrated hydrogen peroxide solution being introduced into the penultimate reaction stage or being divided and a part introduced as a separate stream into one or more of the stages n-1 to 2 and the concentrated formic acid solution being introduced as a separate stream into one or more of the stages n-1, n-2 or n-3 to 2, the oily phase and the hydrogen peroxide/formic acid aqueous phase or acid water phase being separated from one another in a phase separator in each reaction stage after issuing from the reactor and the olefinic phase successively passing through reaction stages 1 to n, while the acid water phase, after reaction stage (n-1), passes successively through the reaction stages (n-2) to 2 in counter flow to the olefin phase and then successively through stages n and 1, while the reaction temperature is maintained between 50.degree. and 80.degree. C. in the reactors and between 15.degree. and 60.degree. C. in the phase separators, and continuously recovering an epoxidized oily compound from reaction stage n and an acid water phase from reaction stage 1.