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The fluorination of mono- and bilayer graphene has been studied by means of ab initio DFT calculations. The stability of CFx systems is found to depend on both the F coverage and the position of the F atoms regarding the C sublattices. When F atoms are chemisorbed onto C atoms belonging to the same sublattice, low coverage is preferred. Otherwise, large F coverage is more stable (up to C4F for oneside fluorination). The di fference of charge distribution between the two carbon sublattices explains this finding that is confirmed by the analysis of the di ffusion barriers. The binding energy of F on bilayer systems is found to be slightly smaller than that on monolayer systems, and electronic decoupling is observed when only one of the layers is exposed to fluorine. (Graph Presented).