The photon statistic of two-photon processes is treated for the general case of two-level systems. After generalizing the generating-function method, we derived the generating function with parameter r (atomic population ratio), its partial differential equation, and equations of factoril moments as well as equations of correlation functions. Analytical solutions were obtained for various values of r. Curves of and g(2) versus τ and r were deduced for three kinds of initial fields. Both the effect of r on photon antibunohing and characteristics photon statistics for two-photon amplifiers are discussed. The photon super bunching is proposed as one of tJie criteria for two-photon amplification.