  We present a systematic study of involutions on the moduli space of $G$-Higgs
bundles over an elliptic curve $X$, where $G$ is complex reductive affine
algebraic group. The fixed point loci in the moduli space of $G$-Higgs bundles
on $X$, and in the moduli space of representations of the fundamental group of
$X$ into $G$, are described. This leads to an explicit description of the
moduli spaces of pseudo-real $G$-Higgs bundles over $X$.
