  In the framework of supersymmetric Grand Unified Theories, the minimal Higgs
sector is often extended by introducing multi-dimensional Higgs representations
in order to obtain realistic models. However these constructions should remain
anomaly-free, which constraints significantly their structure. We review the
necessary conditions for the cancellation of anomalies in general and discuss
in detail the different possibilities for SUSY SU(5) models. Alternative
anomaly free combinations of Higgs representations, beyond the usual
vector-like choice, are identified, and it is shown that their corresponding
beta functions are not equivalent. Although the unification of gauge couplings
is not affected, the introduction of multi-dimensional representations leads to
different scenarios for the perturbative validity of the theory up to the
Planck scale.
