  Discrete gauge symmetries in global intersecting D-brane models constrain the
exact form of the perturbative as well as non-perturbative superpotential. We
derive the complete set of conditions on the existence of discrete Zn gauge
symmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional or
rigid D6-branes on tilted tori, for which global models of particle physics are
known. Several examples of global left-right symmetric and Pati-Salam models
are presented. Some discrete `stringy' Zn symmetries are trivial from the field
theory point of view, while others have not been identified before.
