The paper attempts to combine the Wiener-Bose method for characterizing and synthesizing nonlinear systems with the Ku-Wolf method for analyzing nonlinear systems with random inputs. A simple partition theory is first presented. It is shown that a general nonlinear system can be partitioned into two portions: one linear portion with memory or storage, and one nonlinear portion which may also include linear elements. The partition method, the Taylor-Cauchy transform method, and the transform-ensemble method are developed, and illustrated by an example. It is shown that the output of a nonlinear system to a random input can be expressed as the summation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a_{n}q_{n}(t)</tex> , for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 0, 1, 2,</tex> and so on, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q_{n}(t)</tex> depends upon the form of the functional representation of the modified forcing function or the actuating signal, and a. denotes a set of random variables which are related to the statistics of the random input. Wiener's theory of nonlinear systems is then reviewed. The Wiener-Bose method is outlined as follows. Let the output of a shot-noise generator be the standard probe for the study of non-linear systems. The standard random input is fed to a Laguerre network giving Laguerre coefficients <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u_{1},u_{2},\cdots.</tex> The output of the over-all system is then expressed as Hermite function expansions of the Laguerre coefficients. By the ergodic hypothesis it is then possible to express the output as the summation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{\alpha} V(\alpha) e^{-u^{2}/2}</tex> By taking the time average of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c(t) V(\alpha)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c(t)</tex> represents either the actual output or the desired output, we get the coefficients <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{\alpha}</tex> , which characterize the actual system or the system to be designed. Knowing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{\alpha}</tex> , the synthesis procedure is obtained from the summation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{\alpha} V(\alpha)</tex> . By combining the output <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c(t)</tex> , obtained from the Ku-Wolf analysis, with the output <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V(\alpha)</tex> from the Laguerre network and Hermite function generator, we can get the-characterizing coefficients <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{\alpha}</tex> . It is suggested that the correlation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a_n</tex> , a set of random variables related to the random input, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{\alpha}</tex> , the characterizing coefficients, may shed light on a unified approach for the analysis and synthesis of nonlinear systems with random inputs.