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The theory of random linear systems is extended to systems containing one or more non-independent parameters under the assumption that the parameter processes and the solution process have very widely separated spectra. It is shown that the second product moment of the solution satisfies a linear integral equation which can be solved in closed form in some important special cases. The mean square stability theory of equations containing one purely random coefficient initiated by Samuels .nd Eringen is developed further and extended to systems containing one narrow-band random parameter. Specific mean sjuare stability criteria are worked out for an RLC circuit with capacity variations that are a narrow-band stochastic function.