Introduction (problem statement and relevance). The environmental requirements for vehicle engines becoming more stringent require development and introduction of high-performance turbo chargers. Transition from external to internal varying, namely to the variable nozzles of the turbine, is caused by the necessity to reduce the transient process time during operation of the engine and the vehicle itself.The purpose of the study is development and confi rmation of the methodology (general strategy) for designing and modernization of radial-axial turbines with variable nozzles.Methodology and research methods. The study used the combination of calculation models for the engine itself with preliminary verifi cation based on the results of tests on the engine test bench (AVL BOOST, CRUISE M), gas-dynamic calculation of the turbine stage with determination of geometric parameters of the blade ring, housing (volute) and blade drive mechanism, their geometric modeling (Siemens NX) followed by 3D models export, CFD simulation of the stage fl ow including taking into account the transfer element (with impeller rotation) and generation of the stage curves (AVL FIRE).Scientific novelty and results. Combination (synthesis) of calculation models of different levels makes it possible to determine geometric parameters of the turbocharger turbine with variable nozzles providing high effi ciency (performance factor) of the turbine stage with a simultaneous shift of the maximum torque mode of the engine itself to the area of lower crankshaft rotation rate (along the full-load curve).Practical signifi cance of the paper consists in reduction of the time of design and subsequent refi nement (experimental) works during creation and modernization of turbines with variable nozzles of small-sized turbochargers. The obtained values of relative geometric parameters can be used at the design stage