Based on setting up the mathematic models of the cost sharing problems , the axiomatic systemof the het2 erogeneous cost sharing model is put forward. The axiomatic characters of heterogeneous cost sharing methods fall in2 to three categories : the basic characters , the general characters and the special characters. The necessity of invari2 ance of output scale , demand monotonicity , proportionality and upper bound is discussed by studying some cases. The characters of four typical heterogeneous cost sharing methods —the EANS method , the Aumann2Shapley pricing , the Friedman2Moulin serial cost pricing and the Shapley2Shubik method —are proven