The synthesis of several new 2-, 3- or 4-substituted pyrido[2',3':3,4]pyrazolo[1,5-a]pyrimidines is described. The obtained compounds were tested for their antiproliferative activity in vitro. Two of them: 3-chloro-2-methylpyrido[2',3':3,4]pyrazolo[1,5-a] pyrimidin-4-one [X] and 2,3-cyclopentylpyrido [2',3':3,4] pyrazole[1,5-a]pyrimidin-4-one [XII] revealed weak cytotoxic activity against the cells of human bladder cancer cell lines: LoVo, MCF-7, MES-SA and HCTV29T. The structures of the products II - XII were established on the basis of elemental analysis and spectral data (IR, 1H NMR and MS).