In axial annular flow, the shear stress decreases from its value tau(kappa R) at the inner cylinder to 0 at r=lambda R and increases from then on to tau(R) at the outer cylinder. For plastic fluids with a yield stress tau(c), lambda will be such that flow commences when tau(kappa R)=tau(R)=Ce tau(c). For fluids with position-dependent yield stresses (electro- and magnetorheological fluids are examples), the situation is more complex. While it is possible that yielding and flow occur everywhere, it is also possible that flow occurs only in parts of the fluid-filled space, and a dead zone (region in which the fluid is at rest) close to one of the walls exists. In that case, the fluid will flow no matter how small the applied pressure difference P=Delta p/L is. If P is large enough, the dead zone ceases to exist and flow without any plug is possible. The fluid flows as if no yield stress exists.