Abstract: Series-sequential turbocharging systems and related methods are disclosed herein for boosting the intake pressure of an internal combustion engine, such as a split-cycle engine that operates in accordance with a Miller cycle. In some embodiments, a multi-stage turbocharging system is used in which a small flow capacity turbocharger with an associated turbine bypass valve is incorporated in series with a larger turbocharger and an aftercooler. At low engine speeds, the bypass valve is closed and the small flow capacity turbocharger performs the bulk of the compression work. At high engine speeds, the bypass valve is opened and the larger turbocharger performs the bulk of the compression work. The bypass valve can be modulated when the engine is operated at transitional speeds. Using this series-sequential turbocharging system, the boost and flow range required for optimal efficiency and performance can be met across the engine's speed range.