This is an announcement for the paper "On the structure of asymptotic l_p spaces" by E. Odell, Th. Schlumprecht, and A. Zsak. Abstract: We prove that if X is a separable, reflexive space which is asymptotic l_p, then X embeds into a reflexive space Z having an asymptotic l_p finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of spaces with an asymptotic l_p FDD. More general results of this type are also obtained. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20 Remarks: 32 pages The source file(s), asymptotic-ell-p.tex: 108321 bytes, is(are) stored in gzipped form as 0603063.gz with size 30kb. The corresponding postcript file has gzipped size 143kb. Submitted from: a.zsak@dpmms.cam.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0603063 or http://arXiv.org/abs/math.FA/0603063 or by email in unzipped form by transmitting an empty message with subject line uget 0603063 or in gzipped form by using subject line get 0603063 to: math@arXiv.org.