  The out-of-equilibrium dynamics of the O(N+1) nonlinear sigma model in 1+1
dimensions is investigated in the large N limit. Regarding the nonlinearity as
the effect of a suitable large coupling limit of the O(N+1) \phi^4 model, we
first of all verify that the two limits commute, so that the O(infty) nonlinear
sigma model is uniquely defined. Such model can be completely renormalized also
in the out-of-equilibrium context, allowing us to study the consequences of its
asymptotic freedom on the time evolution far from equilibrium. In particular we
numerically study the spectrum of produced particles during the relaxation of
an initial condensate and find no evidence for parametric resonance, a result
that is consistent with the presence of the nonlinear contraint. Only a weak
nonlinear resonance at late times is observed.
