  In this article we give an equivariant version for the construction of
generic models on presheaves of structures. We deal with first order structures
endowed with a suitable action of some fixed group, say $G$; we call them
$G$-structures. We show that every exact presheaf of $G$-structures
$\mathcal{M}$ has a generic (equivariant) $G$-model $\mathcal{M}^{^{gen}}$.
