We introduce real structures on L-twisted Higgs pairs over a compact Riemann surface equipped with an anti-holomorphic involution, and prove a Hitchin-Kobayashi correspondence for them. Real G-Higgs bundles, where G is a real form of a connected semisimple complex affine algebraic group G C , constitute a particular class of examples of these pairs. The real structure in this case involves a conjugation of G C commuting with the one defining the real form G. We establish a homeomorphism between the moduli space of real G-Higgs bundles and the moduli space of compatible representations of the orbifold fundamental group of X. Finally, we show how real G-Higgs bundles appear naturally as fixed points of certain anti-holomorphic involutions of the moduli space of G-Higgs bundles, that are constructed using the real structures on G C and X.

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