  We work in a general framework where the state of a physical system is
defined by its behaviour under measurement and the global state is constrained
by no-signalling conditions. We show that the marginals of symmetric states in
such theories can be approximated by convex combinations of independent and
identical conditional probability distributions, generalizing the classical
finite de Finetti theorem of Diaconis and Freedman. Our results apply to
correlations obtained from quantum states even when there is no bound on the
local dimension, so that known quantum de Finetti theorems cannot be used.
