We use linear analysis to investigate the slower dynamics of polymer properties in continuous stirred tank olefin polymerization reactors in response to a step change in feed conditions such as catalyst, hydrogen, and monomer feeds. By examining the eigenvalues and the associated eigenvectors of the linearized governing equations, we determine the characteristic time scales for each variable of interest. For the first time, we elucidate that the reason for the slower dynamics in polymer properties and some species for such polymerization reactors is due to the appearance of repeated eigenvalues, which result from sequential events involving one or more slower steps. The results have been validated through both analytical solution and numerical simulation. Catalyst/monomer systems are categorized into different cases based on relative rates of chain transfer to hydrogen and long chain branching. Rules of thumb are developed for each case to determine the time needed for the system to reach steady state in response to a step disturbance, thus allowing for efficient pilot plant trial planning without a priori knowledge of the exact kinetic parameters. The methodology developed in this paper has general implications for the analysis of other complex polymerization systems such as gas-phase olefin polymerization, slurry olefin polymerization, and free radical polymerization carried out in continuous stirred tank reactors.