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The second order moment stability problems for second order linear stochastic systems with colored noise coefficients are studied. Namely, the proposed system equations are ÿ0+2ζν0y0 +[ν02+εx(t)]y0=0 and ÿ0+[2ζν0+εx(t)]y0+ ν02y0=0, where x(t) are the solution processes through the n-th order shaping filter with Gaussian white noise inputs.After the joint Markov models are constructed by Ito's stochastic differential equations with coupling the coefficients processes as state variables, the exact second order moment equations regarding with y0(t)-processes are derived in iteration formulas by applying the Ito's differential rule.Finally, under small ε assumption for the coefficients processes, the approximate necessary and sufficient conditions up to the order of ε3 are obtained via perturbation approach. It is shown that the conditions can be expressed by the power spectrum density functions of the x(t)-processes and only two spectrum point of x(t), 0 and 2ν0√1-ζ2 are related to the obtained stability conditions.
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