Two control strategies for power flow control in hybrid electric vehicles (HEVs) with parallel configuration and a planetary gear system as a power coupling device between the internal combustion engine and the electric machine are proposed in this paper. The aim of both strategies is to determine, for a given driving cycle, an appropriate mixture of the power provided by the two engines. Performance is measured not only in terms of fuel consumption; driving cycle tracking and preservation of energy in the bank of batteries are also considered. The first strategy, named the PGS strategy as it is designed around the planetary gear system, is heuristic, inspired by bang-bang optimal control formulations and has low computational load, while the second is an optimal one derived from Pontryagin's minimum principle (PMP). It is shown that, under appropriate choice of the weighting parameters in the Hamiltonian of the PMP, both strategies give very similar results and, therefore, that the PGS strategy corresponds to a feasible solution to an optimization problem. Both strategies can be implemented in real time, however, the PGS strategy is easier to tune. Tuning of the strategies' parameters is independent of the driving cycle. The power flow control laws are continuous and enforce the use of the internal combustion engine with the maximum possible efficiency. The strategies are tested with simulations of a power train of a hybrid diesel-electric bus subjected to the demands of four representative urban area driving cycles. Although optimization solutions are based on simplified dynamic models, simulation results are verified with more detailed dynamic models of the HEV main subsystems. This allows us to evaluate the accuracy of the results and to verify the hypothesis established in the optimization formulation. Simulation results indicate that both strategies attain good fuel consumption reduction levels.