The stability of a tape/film superconductor of a large aspect ratio is studied by considering the transverse normal zone behavior across a cross-section subjected to an instantaneous thermal disturbance. Different types of behavior in terms of stable superconducting operation, current sharing, quenching, and superconductivity recovery have been identified. A stability criterion was developed based on heat conduction analyses for the current sharing steady state and the quenching steady state. The criterion was tested with the transient stability behavior results for a NbTi superconductor obtained through finite difference method. The effects of operating current density and the composite superconductor's dimensions on the stability performance were also investigated.