A process is described for producing homo-, co- and block copolymers by controlled radical polymerization in aqueous solution, wherein a monomer component (A) consisting of at least one radically polymerizable monomer, an initiator component (B) consisting of at least one radical initiator, a polysaccharide component (C) consisting of at least one cyclic polysaccharide (derivative) and a regulator component (D) consisting of at least one compound of the general formula (Ia) or/and (Ib) are reacted in the presence of water, ##STR00001## in which R.sub.1 to R.sub.6 can each independently denote hydrogen, an optionally substituted C.sub.1 C.sub.20 alkyl residue, C.sub.3 C.sub.8 cycloalkyl residue, C.sub.7 C.sub.34 aralkyl residue or optionally an aromatic C.sub.6 C.sub.14 hydrocarbon residue and R.sub.2 and R.sub.5 can additionally denote polymer residues having an average molecular mass (number average) of 100 to 50,000 Daltons, and at least two but at most four of the residues R.sub.1 to R.sub.6 represent an aromatic hydrocarbon residue. In this manner it is possible to produce polymers with a very narrow molecular weight distribution. Moreover, due to the much lower amounts of initiator and regulator compared to the prior art, the polymers contain only very small amounts of regulator and initiator decomposition products.