The invention relates to a method for producing polyamides, their oligomers or mixtures thereof, optionally containing other reaction products, by reacting aminonitriles or dinitriles and diamines or a mixture containing aminonitrile, dinitrile and diamine and optionally additional polyamide-forming monomers and/or oligomers with water in a reactor (1) with a vertical longitudinal axis. According to said method, the reaction product is exfiltrated from the sump in the reactor (1) and accumulated ammonia and optionally other accumulated low-molecular compounds and water are drawn off via the head (2). The invention is characterised in that the reactor (1) comprises at least two chambers (4) arranged in a longitudinal direction one above the other, that the chambers (4) are separated from one another by liquid-tight floors (5), that each chamber (4) is connected to the one (4) immediately below by a respective liquid overflow (6) and a liquid product stream is drawn off via the liquid overflow (6) of the lowest chamber (4), that the gas chamber (7) above the liquid level in each chamber (4) is connected to the respective chamber (4) lying immediately above it via one or several conduits (8), which open respectively into a gas diffuser (9) comprising orifices (11) for the discharge of gas below the liquid level. The reactor also comprises at least one respective deflector plate (12) positioned vertically around each gas diffuser (9), the upper end of said plate terminating below the liquid level and the lower end terminating above the liquid-tight floor (5) of the chamber (4), thus sub-dividing each chamber (4) into one or more compartments supplied with gas (13) and one or more compartments without gas (14).