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Abstract: In this paper, the output correlation function of nonlinear systems of zero memory with the property of h(lx) characterized by h(k+p)(lx)=lph(k)(lx) (Where h(k)(lx)=(k)h(lx)/xk,l is a real number) is treated, in case of the gaussian process input with zeromathematical expectation.Based on the above characteristics, an ordinary differential equation is derived from Price theorem. Thus a problem of solving the output correlation function of nonlinear system is turned into a problem of solving an ordinary differential equation. The result show that the output correlation functions of nonlinear system of this kind are of the same form. Different h(lx)'s only exert their influences upon coefficients. From the above condition, the characteristic f(x) of the conventional nonlinear system may be expressed in a family of functions which has the performance as mentioned above. by using the results directly, it is easy to obtain a calculating equation concerning the output correlation function of the conventional nonlinear system.