Process for removing polyunsaturated hydrocarbons from olefin-containing C4 hydrocarbon streams that, in addition to C4 hydrocarbons, also contain C5 hydrocarbons in the range between 0.01% and 5% by weight and mercaptans and/or disulfides in the range between 0.01% and 200 ppm by weight, wherein in a first step, at least some of the polyunsaturated hydrocarbons from the olefin-containing C4 hydrocarbon stream are hydrogenated and/or reacted with the mercaptans and/or disulfides from the olefin-containing C4 hydrocarbon stream in a first reaction zone, which consists of one or more reactors connected in parallel and/or in series, wherein the first step is carried out using a first catalyst containing at least two metals of group 10 of the periodic table of the elements, preferably palladium and platinum, and in the presence of hydrogen and in the absence of carbon monoxide and wherein not more than 80 mol% of the available polyunsaturated hydrocarbons from the C4 hydrocarbon stream is hydrogenated and/or reacted in the first step, wherein the molar ratio of hydrogen to polyunsaturated hydrocarbons is between 0.01 and 0.8, in a second step, the polyunsaturated hydrocarbons in the olefin-containing C4 hydrocarbon stream that did not react in the first step are selectively hydrogenated using a second catalyst containing a single metal of group 10 of the periodic table of the elements, preferably palladium, in the presence of hydrogen and carbon monoxide in a second reaction zone, which consists of one or more reactors connected in parallel and/or in series, wherein at least one removal of high boilers takes place between the first step and the second step, and wherein the first and second catalysts are different from one another. in a first step, at least some of the polyunsaturated hydrocarbons from the olefin-containing C4 hydrocarbon stream are hydrogenated and/or reacted with the mercaptans and/or disulfides from the olefin-containing C4 hydrocarbon stream in a first reaction zone, which consists of one or more reactors connected in parallel and/or in series, wherein the first step is carried out using a first catalyst containing at least two metals of group 10 of the periodic table of the elements, preferably palladium and platinum, and in the presence of hydrogen and in the absence of carbon monoxide and wherein not more than 80 mol% of the available polyunsaturated hydrocarbons from the C4 hydrocarbon stream is hydrogenated and/or reacted in the first step, wherein the molar ratio of hydrogen to polyunsaturated hydrocarbons is between 0.01 and 0.8, in a second step, the polyunsaturated hydrocarbons in the olefin-containing C4 hydrocarbon stream that did not react in the first step are selectively hydrogenated using a second catalyst containing a single metal of group 10 of the periodic table of the elements, preferably palladium, in the presence of hydrogen and carbon monoxide in a second reaction zone, which consists of one or more reactors connected in parallel and/or in series, wherein at least one removal of high boilers takes place between the first step and the second step, and wherein the first and second catalysts are different from one another. <EOS>