Abstract A theoretical study on the regulated two-stage turbocharging (R2S) system is conducted based on the equivalent turbocharger concept. Expressions for the equivalent turbine flow area and the equivalent turbocharger efficiency of the R2S system were derived. The equivalent turbine flow area can be used in the analysis of the regulating capacity of the R2S system, according to which the combination of the high and low pressure stage turbochargers is determined. The equivalent turbocharger efficiency gives the criteria for matching the R2S system with diesel engine, which is optimising the exhaust energy distribution between the two-stage turbines to maintain high equivalent turbocharger efficiency. The paper closes with a computational analysis of the characteristic of the R2S system, and the application of the equivalent turbocharger model for matching and optimisation of the R2S system is studied.