An antifreeze concentrate based on alkylene glycols, glycerol and/or 1,3-propanediol comprises a) from 0.05 to 10, preferably from 0.5 to 5, % by weight, based on the total amount of the concentrate, of one or more polyethylene glycols and/or polypropylene glycols and b) from 0.01 to 10, preferably from 0.05 to 10, % by weight, based on the total amount of the concentrate, of one or more carboxamides and/or sulfonamides. Ready-to-use aqueous coolant compositions which contain from 30 to 70, in particular from 40 to 60, % by weight of the concentrate are obtainable from the novel concentrates by dilution with water. Said compositions are distinguished by effective corrosion inhibition in the case of magnesium and magnesium alloys.