Coextrusion is widely used to fabricate multilayered products with each layer providing a separate functionality, including barrier resistance to gases, strength, and printability. Here an analytical model of the coextrusion die flow of two incompressible, viscoplastic fluids in a slit die, subject to nonlinear wall slip and under fully developed and isothermal conditions, is developed to allow the prediction of the steady-state velocity and shear stress distributions and the flow rate versus pressure gradient relationship. The resulting model is applied to the coextrusion of two layers of viscoplastic fluids in a thin rectangular slit die (slit gap, h << slit width, W). The analytical solution recognizes a number of distinct flow conditions (eleven cases) that need to be treated separately. The solutions for all eleven cases are provided along with an apriori identification methodology for the determination of the applicable case, given the shear viscosity and wall slip parameters of the two viscoplastic fluids, the slit geometry and the flow conditions. Simplifications of the model would provide the solutions for the fully developed and isothermal coextrusion flows of any combination of Hershel-Bulkley, Bingham, power-law and Newtonian fluids with or without wall slip at one or both walls of the slit die. POLYM. ENG. SCI., 50:652-664,2010. (C) 2009 Society of Plastics Engineers