The invention relates to the field of the pharmaceutical industry and medicine, and more particularly to novel pegylated derivatives of erythropoiesis factors, and concerns the creation of novel molecules of low-sialylated darbepoetin and polyethylene glycol conjugates of general formula (I) or (II), which have erythropoiesis-stimulating activity, do not cause a sharp drop in glucose, and have improved pharmacokinetic and pharmacodynamic parameters. The invention further relates to drugs containing the claimed formula (I) or formula (II) conjugate, and to pharmaceutical compositions suitable for the treatment and prophylaxis of different anaemias involving the insufficient production of endogenous erythropoietin, said pharmaceutical compositions containing the claimed pegylated low-sialylated darbepoetin conjugates and therapeutically acceptable auxiliary ingredients. The invention further relates to: the use of the formula (I) or formula (II) conjugate to produce a drug that has erythropoiesis-stimulating activity and does not cause a sharp drop in glucose a method for the prophylaxis and/or treatment of anaemias of different origins, which involves administering a therapeutically effective amount of the formula (I) or formula (II) conjugate a container containing the pharmaceutical composition and a set.