  We obtain the operator product expansion of the self-energy in the O(N)
non-linear $\sigma$-model to all orders in the coupling and the large momentum,
and to next-to-leading order in 1/N. In the light of this result we discuss
recent suggestions that there may be additional power corrections from short
distances, associated with defining the coupling constant non-perturbatively.
The non-linear $\sigma$-model provides no evidence for such `non-standard'
power corrections. We also find that the OPE converges for sufficiently large
external momentum, presumably because there are no multi-particle thresholds at
arbitrarily high energies in the 1/N expansion.
