A drive system for a motorised bicycle which omprises an electrical motor for driving the motorised bicycle. The electrical motor has a first electric overload power limit which constitutes a limit for electrical power supplied to the electric motor above which first electric overload power limit the electric motor reaches a thermal overload on a long term basis, A battery is provided for supplying electric drive power to the electrical motor for driving the bicycle.. The battery has a second electric overload power limit which constitutes a limit of electric power drawn from the battery above which second electric overload power limit the battery reaches a thermal overload on a long term basis. A control unit is connected to the electrical motor and the battery for controlling the supply of the electric drive power from the battery to the electrical motor and for exclusively selecting a first level of the electric drive power from a first range of electric drive power levels. The first range of electric drive power levels has a maximum power level being equal to or smaller than the first electric overload power limit and/or the second electric overload power limit.