Fuel optimal lock-up transients for a heavy duty series hybrid electric vehicle are studied. A mean value engine model is used together with numerical optimal control to investigate the interplay between electric machine, gearbox and engine with its turbocharger dynamics in particular how they influence the manner and rate at which the engine should be controlled in order to reach a synchronized speed with the gear-box, enabling lock-up. This is studied both for prescribed gear-box speeds, simulating a mechanical transmission, and with gear-box speed an optimization variable, simulating a continuously variable transmission. The optimal engine transients and their duration are seen to be dictated by the stationary efficiency of the different drivetrain modes, showing that the ratio between the efficiencies of the electric and mechanical path dominates the dynamics and have a greater effect than the engine and turbocharger dynamics. In particular the transition between the modes is as fast as possible when the conventional powertrain is the most efficient and as slow as possible when the engine-generator set is more efficient. This points out that the stationary efficiency maps can be used in a central way for the control design of lock-up transients. (c) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.