  We consider the phenomenon of classicalization in nonlinear sigma models with
both positive and negative target space curvature and with any number of
derivatives. We find that the theories with only two derivatives exhibit a weak
form of classicalization, and that the quantitative results depend on the sign
of the curvature. Nonlinear sigma models with higher derivatives show a strong
form of the phenomenon which is independent of the sign of curvature. We argue
that weak classicalization may actually be equivalent to asymptotic safety,
whereas strong classicalization seems to be a genuinely different phenomenon.
We also discuss possible ambiguities in the definition of the classical limit.
