Linear stability analysis has been applied to a coextrusion fiber spinning flow that consists of a Newtonian fluid as a core layer and a Phan-Thien/Tanner (PTT) fluid as a skin layer. These two chosen fluids show entirely different rheological behaviors. The stability of this coextrusion system was affected by the choice of three characteristic parameters : the skin layer fraction (f), the extensional parameter (epsilon), and the shear thinning parameter (xi) in the Phan-Thien/Tanner model. The linear stability results indicate that the viscoelastic skin layer (PTT fluid) has a stabilizing effect that delays the onset of draw resonance. Under fixed compositions (f is fixed), the stability envelopes changed from upturned curves to flattened ones as extensional force dominated the system. The neutral stable curves closed to the horizontal line at a critical draw ratio of around 20, showing similar behavior to a Newtonian fluid where the system has a very high Deborah number or it is dominated by shear thinning effects.