Our previous treatment of noise in the nonequilibrium steady state is extended to include nonstationary processes, and processes for which the quasilinear approximation is inadequate. By use of backward-equation methods, we show that $M_0(a_0, t, t_0)=〈〉\left(\exp \left[-\int {t_0}^{t}Q\left(a\right(s), t-s) \mathrm{ds}\right]\right)$ subject to $\mathrm{a}\left(t_0\right)={\mathrm{a}}_0$ obeys the differential (integral) equation: $\frac{\partial M_0(a_0, t, t_0)}{\partial t_0}=\left[Q\right(a_0, t-t_0)-\Sigma \stackrel{\infty }{n=1\mathrm{}}{\mathrm{D}}_n(a_0, t_0):{\left(\frac{\partial }{\partial a_0}\right)}^n]M_0,$ where the ${\mathrm{D}}_n$ are the $n\mathrm{th}$-order diffusion coefficients of the $\mathrm{a}\mathrm{}\left(s\right)\mathrm{}$ process, and $Q\left(\mathrm{a}\mathrm{}\right(s), s)$ is an arbitrary function of a and $s$. The choice $D_n=0\mathrm{}$, $n>\mathrm{}2\mathrm{}$, $D_2=D$ $D_1\mathrm{}\left(a\right)=-\Lambda a$ makes $a\left(s\right)\mathrm{}$ an Ornstein-Uhlenbeck (O.U.) process, i.e., white noise that has been filtered through an $\mathrm{RC}$ network with time constant $\frac{1}{\Lambda }$. The choice $Q\left(a\right(s), s)=k(t-s)\mathrm{}{\mathrm{}\left[a\right(s\left)\right]}^2$ squares the output and applies the time smoothing $k(t-s)\mathrm{}$. For $k\left(s\right)=\exp (-2\mathrm{}\beta s)$ [time smoothing through an $\mathrm{RC}$ network with time constant $\left(\frac{1}{2\beta }\right)$], an explicit solution is obtained for the characteristic function $M_0$. For arbitrary positive $k\left(s\right)\mathrm{}$, we show that $M_0$ becomes independent of $a_0$ as $t\to \infty$ if $k\left(\infty \right)=0\mathrm{}$, and $M_0$ becomes stationary if $\Lambda >0\mathrm{}$ and $\int 0^{\infty }k\left(u\right)\mathrm{} \mathrm{du}<\mathrm{}\infty .$

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