Recent observations of an unexpectedly high incidence of bright Leonid meteors about 16 hours before the predicted maximum of the main shower are explained by the ejection of dust grains into the 5/14 mean-motion resonance with Jupiter, principally during the perihelion passage of Comet 55P/Tempel-Tuttle in 1333. The dynamical evolution of resonant grains has the following properties: first, they do not spread uniformly around the orbit, but instead librate about a resonance centre within the main stream; secondly, these resonant zones contain a much higher space density of particles than the background stream, with the particle density approaching that of recently ejected cometary grains; and thirdly, differential precession between the cometary orbit and the orbits of resonant particles may lead to meteor storms at unexpected times, possibly far removed from that of the normal shower. The presence of resonant dust grains leads to a complex structure within the Leonid meteoroid stream, and is an important general feature of meteoroid streams associated with Halley-type comets, themselves often trapped for long periods in mean-motion resonances.