This thesis focused on the stability analysis for the linear differential equation with two delays: y(_) + A y(_) + By(_ _ 1) + Cy(_ _ R) = 0. (1) This equation has four parameters, and its analysis is surprisingly complex. We build upon previous work of Joseph Mahaffy and Timothy Busken in locating the stability region. Their earlier work provided the theoretical framework and important numerical results supporting the idea that when the delay R is rational, the region of stability is enlarged. Previously developed computer programs demonstrated how the region of stability in the ABC-parameter space evolves with changing R. This thesis provides some analytic proofs to support the enlarged region for R = _. Our analysis shows how sensitive the region of stability is to the delay, R. This work may assist mathematical modelers with the sensitivity analysis and complex solutions observed for some models with multiple delays.