A eutectic dendrite growth model in which the interface, solute diffusion in the liquid, and triple-junction (TJ) are under non-equilibrium conditions is proposed for undercooled binary alloys. This model, compared with previous work, is applicable to concentrated alloys. Application of the model to the undercooled Ag-Cu eutectic alloy obtained a good agreement between model predictions and experimental results. An upper limit on the eutectic growth velocity is predicted above which migration of TJ is not kinetically possible and a transition from co-operative eutectic growth to single-phase growth occurs for concentrated alloys and dilute alloys with linear liquidus and solidus, respectively.