Fukui functions have been calculated for large numbers of organic molecules, and were found to always be positive. Numeric and algebraic considerations allowed the identification of several boundary conditions for negative values for Fukui functions. Negative Fukui functions are found to be very unlikely, except when very short interatomic distances are present. Recent hypotheses concerning the occurrence of negative Fukui functions are strongly supported by the present approach. (C) 2003 American Institute of Physics.