An electric power steering system has a steering mechanism connecting a steering wheel to the road wheels of the vehicle, typically via a steering column 5. An electric motor 1 is connected to the steering mechanism. The system has column torque and column position sensors 6, 10 which generate signals corresponding respectively to the carried column torque and the angular position of the steering wheel or a steering column, and a processor 7 which receives the torque signal and column angle signals and generates a torque demand signal. Processor 7 uses a boost curve to determine an assistance torque based on the column torque signal, and determines a friction compensating torque signal based on observations of the column torque and column angle signals over time and on an estimate of static friction in the steering mechanism. A torque demand signal is produced as a function of the friction compensating torque and assistance torque signals. The friction compensating torque signal assists a driver in overcoming static and/or kinetic friction in the steering mechanism.