An electron beam transport system for controlling the position of two different electron beams comprises: a main electron beam transport module; a first input electron beam transport module; a second input electron beam transport module; and a controller. The main electron beam transport module comprises a beam monitoring device disposed at a measurement position. The first input electron beam transport module comprises a first actuator for applying a perturbation to a transverse position of a first electron beam at a first actuation point. The second input electron beam transport module comprises a second actuator for applying a perturbation to a transverse position of a second electron beam at a second actuation point. The controller is operable to receive a signal from the beam monitoring device and to send control signals to the first actuator and the second actuator. The controller is operable to determine a first quantity indicative of a difference in a transverse position of the first and second electron beams and a second quantity indicative of an average transverse position of the first and second electron beams. The controller is further operable to control the trajectories of the first and second electron beams independently by implementing a first control loop that iteratively attempts to reduce the first quantity by using the first actuator to perturb a trajectory of the first electron beam, and a second control loop that iteratively perturbs a trajectory of the second electron beam using the second actuator such that the average transverse position of the two different electron beams moves towards a desired transverse position.