That high-order resonances may be involved in determining rates of vibrational relaxation in highly excited molecules has been recognized for some time. In this paper, high-order resonances are shown to play a central role in establishing the transition to ergodic flow, which we call the quantum ergodicity transition, at low energy in many-dimensional systems. The location of the transition to global vibrational flow in a system of coupled nonlinear oscillators is found to be generally sensitive to high-order resonances. On the other hand, except immediately above the transition, rates of flow once established depend primarily on the familiar low-order terms until the molecule reaches much higher excitation. Both the orders of resonant coupling terms in the vibrational Hamiltonian important in determining the transition to ergodicity, and the orders relevant for determining vibrational relaxation rates in large molecules are found to scale in a simple way with the strength of resonant coupling terms and the size of the molecule.