This is an announcement for the paper "The Daugavet equation for bounded vector valued functions" by Stefan Brach, Enrique A. Sanchez Perez and Dirk Werner. Abstract: Requirements under which the Daugavet equation and the alternative Daugavet equation hold for pairs of nonlinear maps between Banach spaces are analysed. A geometric description is given in terms of nonlinear slices. Some local versions of these properties are also introduced and studied, as well as tests for checking if the required conditions are satisfied in relevant cases. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B25, 46B80 Submitted from: werner@math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.04185 or http://arXiv.org/abs/1507.04185