This is an announcement for the paper "Strictly singular operators in asymptotic $\ell_p$ Banach spaces" by Anna Pelczar-Barwacz. Abstract: We present condition on higher order asymptotic behaviour of basic sequences in a Banach space ensuring the existence of bounded non-compact strictly singular operator on a subspace. We apply it in asymptotic $\ell_p$ spaces, $1\leq p<\infty$, in particular in convexified mixed Tsirelson spaces and related asymptotic $\ell_p$ HI spaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B06 Remarks: 19 pages Submitted from: anna.pelczar@im.uj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.5874 or http://arXiv.org/abs/1109.5874