  We investigate structure functions in the 2-dimensional (asymptotically free)
non-linear O(n) sigma-models using the non-perturbative S-matrix bootstrap
program. In particular the exact small (Bjorken) x behavior is derived.
Structure functions in the special case of the n=3 model are accurately
computed over the whole x range for $-q^2/M^2<10^5$, and some moments are
compared with results from renormalized perturbation theory. Some results
concerning the structure functions in the 1/n approximation are also presented.
