This is an announcement for the paper "Finite order spreading models" by S.A. Argyros, V. Kanellopoulos and K. Tyros. Abstract: Extending the classical notion of the spreading model, the $k$-spreading models of a Banach space are introduced, for every $k\in\mathbb{N}$. The definition, which is based on the $k$-sequences and plegma families, reveals a new class of spreading sequences associated to a Banach space. Most of the results of the classical theory are stated and proved in the higher order setting. Moreover, new phenomena like the universality of the class of the 2-spreading models of $c_0$ and the composition property are established. As consequence, a problem concerning the structure of the $k$-iterated spreading models is solved. Archive classification: math.FA Remarks: 41 pages, no figures Submitted from: chcost@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1105.2732 or http://arXiv.org/abs/1105.2732