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Consistent heterotic orbifold vacua, includingnonperturbative information, can be constructed.Generically, the usual modular invariance constraintsare violated and thus, anomalies are expected. However, five-branes do appear in the correct proportionjust to ensure the consistency of the full theory. Wefirst exemplify the situation in six dimensions, N = 1,where strong-coupling effects, implying the presence of five-branes, are better known.Explicit N = 1 models in D = 4, essentially inheritedfrom six dimensions, are then presented. In particularwe show concrete examples of models which exhibit nonperturbative transitions leading to gaugeenhancement and/or to a change in the number of chiralgenerations.

We study in detail the structure of Grand Unified Theories derived as the low-energy limit of orbifold four-dimensional strings. To this aim, new techniques for building level-two symmetric orbifold theories are presented. New classes of GUTs in the context of symmetric orbifolds are then constructed. The method of permutation modding is further explored and SO(10) GUTs with both 45- or 54-plets are obtained. SU(5) models are also found through this method. It is shown that, in the context of symmetric orbifold SO(10) GUTs, only a single GUT Higgs, either a 54 or a 45, can be present and it always resides in an order-two untwisted sector. Very restrictive results also hold in the case of SU(5). General properties and selection rules for string GUTs are described. Some of these selection rules forbid the presence of some particular GUT-Higgs couplings which are sometimes used in SUSY-GUT model building. Some semi-realistic string GUT examples are presented and their properties briefly discussed.