We study the prospects for constructing finite grand unified theories using softly broken N = 2 global supersymmetry. The requirement that the supersymmetry breaking scale be of order 103−104 GeV and that the mixing between the observed light fermions and the mirror fermions present in N = 2 theories be small («mW), make it difficult to construct finite grand unified theories based on a large class of simple groups with a realistic symmetry breaking pattern.