This is an announcement for the paper "Weak compactness of almost limited operators" by A. Elbour, N. Machrafi, and M. Moussa. Abstract: The paper is devoted to the relationship between almost limited operators and weakly compacts operators. We show that if $F$ is a $\sigma $-Dedekind complete Banach lattice then, every almost limited operator $T:E\rightarrow F $ is weakly compact if and only if $E$ is reflexive or the norm of $F$ is order continuous. Also, we show that if $E$ is a $\sigma $-Dedekind complete Banach lattice then the square of every positive almost limited operator $ T:E\rightarrow E$ is weakly compact if and only if the norm of $E$ is order continuous. Archive classification: math.FA Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65 (Secondary) Remarks: 5 pages Submitted from: azizelbour@hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.3348 or http://arXiv.org/abs/1403.3348