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iii Analysis of stability for delay differential equations (DDEs) is a tool in a va-riety of fields such as nonlinear dynamics in physics, biology, and chemistry, engineering and pure mathematics. Stability analysis is based primarily on the eigenvalues of a discretized system. Situations exist in which practical and numerical results may not match expected stability inferred from such ap-proaches. The reasons and mechanisms for this behavior can be related to the eigenvectors associated with the eigenvalues. When the operator associated to a linear (or linearized) DDE is significantly non-normal, the stability analysis must be adapted as demonstrated here. Example DDEs are shown to have so-lutions which exhibit transient growth not accounted for by eigenvalues alone. Pseudospectra are computed and related to transient growth