Studies of a broad bandwidth, two-colour FEL amplifier using one monoenergetic electron beam are presented. The two-colour FEL interaction is achieved using a series of undulator modules alternately tuned to two well-separated resonant frequencies. Using the broad bandwidth FEL simulation code Puffin, the electron beam is shown to bunch strongly and simultaneously at the two resonant frequencies. Electron bunching components are also generated at the sum and difference of the resonant frequencies.