  Let $p: Y \ra X$ be a Galois cover of smooth projective curves over $\CC$
with Galois group $\Gamma$. This paper is devoted to the study of principal
orthogonal and symplectic bundles $E$ on $Y$ to which the action of $\Gamma$ on
$Y$ lifts. We notably describe them intrinsically in terms of objects defined
on $X$ and call these objects parahoric bundles. We give necessary and
sufficient conditions for the non-emptiness of the moduli of stable (and
semi-stable) parahoric special orthogonal, symplectic and spin bundles on the
projective line $\PP^1$.
