These proceedings deal with a selection of papers presented at the 9th International Conference CASYS'09, on Computing Anticipatory Systems, 3-8 August 2009, held at HEC Management School - University of Liege, Liège, Belgium. The content of these proceedings deals with the most recent theoretical developments and applications in the modeling and computing of anticipation in any field of natural and artificial systems. A computing anticipatory system is a system that computes its current states in taking into account its past and present states but also its potential future states. Strong anticipation refers to an anticipation of events built by or embedded in a system. Weak anticipation refers to an anticipation of events predicted or forecasted from a model of a system.This volume contains Invited Papers and all the peer reviewed papers that received a best paper award at CASYS '09. The interdisciplinary outstanding topics of these proceedings are readable by researchers and scientists with a university background.