A linearized unsteady state flow model is developed for two counter-currently flowing liquids in an un-agitated perforated plate liquid-liquid column contactor. The model is based on the simultaneous solution of dynamic conservation equations and linearized hydrodynamic constitutive equations relating pressure drops and dispersed phase holdups to flow rates. Analytical expressions are obtained for the dynamic responses of inter-stage continuous and dispersed phase flow rates, inter-stage holdups, and level of the top interface to changes in the light liquid and heavy liquid inflow rates to the column. The system's dynamic behavior is vividly demonstrated through a set of typical frequency and transient response computations. Owing to the interaction between the dynamics associated with the flow of the two liquids, the frequency responses of the flow rates and holdups of the two phases are characterized by resonance peaks and non-minimum phase behavior. (c) 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.