A turbocharger has a turbine rotor (14) in a housing (10) with an exhaust inlet (11) and outlet(12). The turbine shaft (20) is supported by radial bearings (21,22) on the housing. The compressor rotor (19) is at the other end of the turbine shaft in its own housing (18). A bypass passage (16) in the turbine housing connects the exhaust inlet and outlet and contains a valve (17) which opens or closes according to the charging pressure. There is a nozzle (15) on the turbine housing near the rotor. The bypass passage has a spiral chamber whose cross-section is gradually reduced in the rotation direction of the rotors. Its opening to the exhaust outlet is circular around the peripheral surface of the nozzle.