The phenomenon of slow light is interesting not only from a fundamental physics standpoint, but also because it introduces the possibility of new applications in telecommunications. For a practical slow-light device, the important features are bandwidth, range of wavelength tunability and size, rather than the absolute slowdown factor achieved. Slow light can be achieved in three main ways: through quantum interference effects, which can slow the speed of light down to several metres per second, albeit within a very narrow bandwidth; by using photonic crystals, which are able to slow light over large bandwidths but with much smaller slowdown factors; and by using stimulated Brillouin or Raman scattering. Surface plasmon polaritons have the advantage that they can overcome the diffraction limit of light in a microchip-sized device. Increases in the propagation lengths of surface plasmon polaritons and the feasibility of all-optical wavelength tunability have been reported. Here we report the observation of slow, femtosecond surface-plasmon-polariton wavepackets. We show that a highly compact (55 microm length) plasmonic structure is able to achieve an effective slowdown factor of two over a 4 THz bandwidth. These results will increase the scope of photonic devices based on surface plasmon polaritons.