EN
We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set $SM_{ξ}^{w}(X)$ of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if $SM_{ξ}^{w}(X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $SM_{ξ}^{w}(X)$ is uncountable, then it contains an antichain of size continuum.