Combinatorial problems can be modeled as constraint satisfaction problems (CSP). Modeling and resolution of CSP is often strengthened by global constraints (e.g., Alldiff constraint). We propose a formal system and some propagation rules for reducing domains of variables appearing in several Alldiff global constraints. We illustrate our approach on the well-known Sudoku puzzle which presents 27 overlapping Alldiffconstraints in its 9 x 9 standard size. We also present some preliminary results we obtained in CHR and GeCode.