This is an announcement for the paper "Weakly countably determined spaces of high complexity" by Antonio Aviles. Abstract: We prove that there exist weakly countably determined spaces of complexity higher than coanalytic. On the other hand, we also show that coanalytic sets can be characterized by the existence of a cofinal adequate family of closed sets. Therefore the Banach spaces constructed by means of these families have at most coanalytic complexity. Archive classification: math.FA Mathematics Subject Classification: 46B26 Citation: Stud. Math. 185, No. 3, 291-303 (2008) Remarks: This version differs from the published in Studia Mathematica in that The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0852 or http://arXiv.org/abs/0903.0852 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0852 or in gzipped form by using subject line get 0903.0852 to: math@arXiv.org.