A two‐dimensional magnetohydrodynamic code that includes resistivity and viscosity has been used to study the growth ofm=0 perturbations of a Z pinch in which the current increases with time. Stability for all wave numbers was found when the productSRwas less than about 1000, whereSis the Lundquist number andRis the Alfve´n–Reynolds number. SinceSRdepends only on the line densityN, the stability criterion translates asN<2×1016ions cm−1(deuterium). This is two to three orders of magnitude smaller than the line density of fiber pinch experiments that have shown anomalous stability, and it is concluded that viscoresistive effects are inadequate to account for these observations.