This is an announcement for the paper “On Weak Supercyclicity I” by C.S. Kubrusly<https://arxiv.org/find/math/1/au:+Kubrusly_C/0/1/0/all/0/1>, B.P. Duggal<https://arxiv.org/find/math/1/au:+Duggal_B/0/1/0/all/0/1>. Abstract: This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.08091