We discuss the gauge hierarchy problem in theories that posses an additional discrete symmetry. As examples, we consider two models based on the gauge groups U(1)L×U(1)Rand SU(2)L×SU(2)R×U(1), with parity transformation as the discrete symmetry. By employing a minimal choice of Higgs multiplets there is no freedom, in the semi-classical approximation, to arrange for an arbitrary hierarchy. Either one has a left-right symmetric phase (no hierarchy) or a totally asymmetric phase (infinite hierarchy). It is shown that radiative corrections, à la Coleman-Weinberg, do not smooth out the transition region separating the two phases. A finite gauge hierarchy is not realized. © 1979.