The theory of linear passive systems, developed by KÖNIG and MEIXNER, is extended to the case where the input is not a well determined function of time but rather a stochastic process. In this case the answer of the system generally will also be a stochastic process. The input and output processes are connected by a linear passive transformation (LPT). Some examples are given of physical systems which may be described by LPT of stochastic processes. General properties of the mean value and the dispersion of the output process are derived.