Sawtooth behaviour has been investigated in plasmas heated with off-axis neutral beam injection (NBI) in ASDEX Upgrade [A. Herrmann and O. Gruber, Fusion Sci. Technol. 44, 569 (2003)] and the Mega-Ampere Spherical Tokamak (MAST) [A Sykes et al., Nucl. Fusion 41, 1423(2001]. Provided that the fast ions are well confined, the sawtooth period is found to decrease as the neutral beam is injected further off-axis. Drift kinetic modelling of such discharges qualitatively shows that the passing fast ions born outside the q = 1 rational surface can destabilise the n = 1 internal kink mode, thought to be related to the sawtooth instability. This effect can be enhanced by optimising the deposition of the off-axis beam energetic particle population with respect to the mode location.