We link the formation of an odd-frequency paired state to the developm
ent of an anomalous three-body scattering amplitude. We show how a sim
ple ansatz leads to a simple realization of odd-frequency superconduct
ivity in a mean-field model of the Kondo lattice. The gapless quasipar
ticles of this state are equal mixtures of particle and hole at zero f
requency and their spin and charge coherence factors vanish, unlike co
nventional even-paired BCS quasiparticles. We discuss the difficulties
this and other models face in attempting to explain experiments in he
avy-fermion superconductors.