  We investigate the energy dependence of inelastic processes in systems which
possess Efimov states. We consider the three-body recombination rate $K_3$
where three free atoms interact to produce an atom--dimer pair, and the
relaxation rate $K_{\rm rel}$ where an atom quenches a weakly bound state of a
dimer near an Efimov resonance to more deeply bound levels. Using a model
capturing the key features of the Efimov problem, we identify new energy
regimes for $K_3$, namely the NTR (Near Threshold Resonance) regime behavior
$E^{-2}$ for negative scattering lengths and the NTS (Near Threshold
Suppression) regime behavior $E^2$ for positive scattering lengths. We also
confirm a previously found oscillatory behavior of $K_3$ at higher energy $E$.
Finally, we find that $K_{\rm rel}$ behaves as $E^{-1}$ in the NTR regime.
