Disclosed is a process for preparing copolymer dispersions made of alkylene oxides and glycidyl ethers according to formula (I) in which R1 is hydrogen or a C1-C4-alkyl radical, R2 and R4 are an alkyl or aryl radical having 1 to 30 carbon atoms, and R3 is an alkyl or aryl radical having 1 to 50 carbon atoms, which may also contain heteroatoms. A is an alkylene unit having 2 to 6 carbon atoms. In formula (1), x is a number from 0 to 10, y is a number from 0 to 10, n is a number from 0 to 100, k is a number from 1 to 100, R5 is an acid group or hydrogen, and m is a number from 1 to 500, with the proviso that (y+n) must be at least 1.