This is the first of a two-part simulation study that discusses the application of a multimode combustion engine in a mild hybrid electric vehicle (HEV). The torque assist, offered by the electric motor, can be used to extend the residence time in the homogeneous charge compression ignition (HCCI) regime, before returning to spark-ignition (SI) combustion. To enable multimode operation in the HEV, the supervisory control strategy has to maintain the battery's state-of-charge while accounting for the SI/HCCI combustion mode switch. In this study four supervisors are discussed which extend the baseline equivalent consumption minimization strategy by the mode switching decision. (C) 2016 Elsevier Ltd. All rights reserved.