This is an announcement for the paper "Local automorphisms of the Hilbert ball" by Bernhard Lamel. Abstract: We prove an analogue of Alexander's Theorem for holomorphic mappings of the unit ball in a complex Hilbert space: Every holomorphic mapping which takes a piece of the boundary of the unit ball into the boundary of the unit ball and whose differential at some point of this boundary is onto is the restriction of an automorphism of the ball. We also show that it is enough to assume that the mapping is only Gateaux-holomorphic. Archive classification: Complex Variables; Functional Analysis Mathematics Subject Classification: 32H12, 46G20, 46T25, 58C10 The source file(s), L_hilbertball/definitions.tex: 3255 bytes, L_hilbertball/hilbertball2.bbl: 1011 bytes, L_hilbertball/hilbertball2.tex: 24133 bytes, is(are) stored in gzipped form as 0612688.tar.gz with size 10kb. The corresponding postcript file has gzipped size 89kb. Submitted from: bernhard.lamel@univie.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.CV/0612688 or http://arXiv.org/abs/math.CV/0612688 or by email in unzipped form by transmitting an empty message with subject line uget 0612688 or in gzipped form by using subject line get 0612688 to: math@arXiv.org.