This is an announcement for the paper "On nested sequences of convex sets in a Banach space" by Jesus M. F. Castillo, Manuel Gonzalez and Pier Luigi Papini. Abstract: In this paper we study different aspects of the representation of weak*-compact convex sets of the bidual $X^{**}$ of a separable Banach space $X$ via a nested sequence of closed convex bounded sets of $X$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: This paper is to appear in Studia Mathematica Submitted from: castillo@unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6725 or http://arXiv.org/abs/1406.6725