This is an announcement for the paper "Common fixed points of commutative semigroups of nonexpansive mappings" by T. Suzuki. Abstract: In this paper, we discuss characterizations of common fixed points of commutative semigroups of nonexpansive mappings. We next prove convergence theorems to a common fixed point. We finally discuss nonexpansive retractions onto the set of common fixed points. In our discussion, we may not assume the strict convexity of the Banach space. Archive classification: Functional Analysis Mathematics Subject Classification: 47H20 Remarks: 18 pages The source file(s), suzuki2.tex: 57526 bytes, is(are) stored in gzipped form as 0404428.gz with size 13kb. The corresponding postcript file has gzipped size 77kb. Submitted from: suzuki-t@mns.kyutech.ac.jp The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404428 or http://arXiv.org/abs/math.FA/0404428 or by email in unzipped form by transmitting an empty message with subject line uget 0404428 or in gzipped form by using subject line get 0404428 to: math@arXiv.org.