The flow of chemically reactive non-Newtonian materials, such as bio-polymers, and acrylates, in a fully intermeshing, co-rotating twin-screw extruder is numerically investigated. A detailed study of the system transient behavior is carried out. The main transient aspects, including response time, variation of system variables, and instability of operation, are studied for both single- and twin-screw extruders, since single-screw extruder modeling closely approximates the region away from the intermeshing zone in a twin-screw extruder. The effect of a time-dependent variation in the boundary conditions is studied. The coupling due to conduction heat transfer in the screw barrel is found to be very important and is taken into account for single-screw extruders. in the absence of this conjugate coupling, the response time is much shorter. Several other interesting trends are obtained with respect to the dependence of the transient response on the materials and operating conditions. Steady state results are obtained at large time. The calculated velocity distributions in the screw channel are compared with experimental results in the literature for steady state flow and good agreement has been obtained. The calculated results for transient transport agree with the few experimental observations available on this system. Chemical reaction, leading to chemical conversion of the material, is also considered and the resulting effects on the flow and transport determined. These results will be useful in the design, control and optimization of polymer extrusion processes.