In this talk the stability of time dependent flows is examined extending methods recently developed for analyzing stability of time independent flows. These methods approach the stability problem by analyzing the non-normality of the underlying dynamical operator. For both autonomous and non-autonomous operators this approach leads to identification of a complete set of optimal perturbations ordered according to extent of growth over a chosen time interval as measured in a chosen norm. The long time asymptotic structure in the case of an autonomous operator is the norm independent least stable normal mode while in the case of the non-autonomous operator it is the first Lyapunov vector which is also norm independent and grows exponentially in the mean at the rate of the first Lyapunov exponent. While structure, growth rates and energetics of the normal mode and therefore the asymptotic stability properties of autonomous systems are easily accessible through eigenanalysis of the associated dynamical operator, analogous information for the Lyapunov vector is less readily obtained. In this work the stability of time dependent deterministic and stochastic dynamical operators is examined in order to obtain a better understanding of the dynamics of asymptotic instability in time dependent systems. It is found that the physical mechanism producing asymptotic error growth in time dependent systems can be traced to the generic non-normality of the non-autonomous operator. Implications for the Lyapunov exponent magnitude and associated vector structure in tangent linear equations are discussed.