Process for the preparation of polyether carbonate polyols from one or more H-functional starter substances, one or more alkylene oxides and carbon dioxide in the presence of a double metal cyanide catalyst and in the presence of at least one additive A), characterized in that (α) the H-functional starter substance or a mixture of at least two H-functional starter substances is initially introduced into the reaction vessel, the DMC catalyst being added to the H-functional starter substance or the mixture of at least two H-functional starter substances, (β) for the activation, a part amount (based on the total amount of the amount of alkylene oxides employed in the activation and copolymerization) of one or more alkylene oxides is added to the mixture resulting from step (α), it being possible for this addition of a part amount of alkylene oxide optionally to be carried out in the presence of CO 2, and the temperature peak which occurs due to the subsequent exothermic chemical reaction and/or a drop in pressure in the reactor then in each case being awaited, and it also being possible for step (β) to be carried out several times for the activation, (γ) one or more alkylene oxides and carbon dioxide are added to the mixture resulting from step (β) ("copolymerization"), it being possible for the alkylene oxides employed for the copolymerization to be identical to or different from the alkylene oxides employed in the activation, wherein the additive A) is added in step (α) to the H-functional starter substance or the mixture of at least two H-functional starter substances and/or the additive A) is added in step (β) to the part amount of one or more alkylene oxides to the mixture resulting from step (α), and wherein the additive A) is at least one compound chosen from the group consisting of - sterically non-hindered phenols according to formula wherein g = 1 or 2 and R i represents an amino, bromo, chloro, cyano, iodo, methoxy, methyl or nitro group; - catechols according to formula (IIIa) and pyrocatechols according to formula (IIIb) wherein g is as defined above R j represents an acetamido, amino, bromo, n-butyl, iso-butyl, tert-butyl, chloro, cyano, ethoxy, ethyl, fluoro, iodo, methoxy, methyl, nitro, iso-propyl or n-propyl group; - phenothiazines, - benzothiazoles, - phenoxazines, - 2, 2, 6, 6 -tetramethylpiperidine 1-oxyl and - nitro styrenes. (α) the H-functional starter substance or a mixture of at least two H-functional starter substances is initially introduced into the reaction vessel, the DMC catalyst being added to the H-functional starter substance or the mixture of at least two H-functional starter substances, (β) for the activation, a part amount (based on the total amount of the amount of alkylene oxides employed in the activation and copolymerization) of one or more alkylene oxides is added to the mixture resulting from step (α), it being possible for this addition of a part amount of alkylene oxide optionally to be carried out in the presence of CO 2, and the temperature peak which occurs due to the subsequent exothermic chemical reaction and/or a drop in pressure in the reactor then in each case being awaited, and it also being possible for step (β) to be carried out several times for the activation, (γ) one or more alkylene oxides and carbon dioxide are added to the mixture resulting from step (β) ("copolymerization"), it being possible for the alkylene oxides employed for the copolymerization to be identical to or different from the alkylene oxides employed in the activation, - sterically non-hindered phenols according to formula wherein g = 1 or 2 and R i represents an amino, bromo, chloro, cyano, iodo, methoxy, methyl or nitro group; g = 1 or 2 and R i represents an amino, bromo, chloro, cyano, iodo, methoxy, methyl or nitro group; - catechols according to formula (IIIa) and pyrocatechols according to formula (IIIb) wherein g is as defined above R j represents an acetamido, amino, bromo, n-butyl, iso-butyl, tert-butyl, chloro, cyano, ethoxy, ethyl, fluoro, iodo, methoxy, methyl, nitro, iso-propyl or n-propyl group; - phenothiazines, - benzothiazoles, - phenoxazines, - 2, 2, 6, 6 -tetramethylpiperidine 1-oxyl and - nitro styrenes. g is as defined above R j represents an acetamido, amino, bromo, n-butyl, iso-butyl, tert-butyl, chloro, cyano, ethoxy, ethyl, fluoro, iodo, methoxy, methyl, nitro, iso-propyl or n-propyl group; - phenothiazines, - benzothiazoles, - phenoxazines, - 2, 2, 6, 6 -tetramethylpiperidine 1-oxyl and - nitro styrenes. - phenothiazines, - benzothiazoles, - phenoxazines, - 2, 2, 6, 6 -tetramethylpiperidine 1-oxyl and - nitro styrenes.