In this talk we present some recent results on the convergence of nonlinear Dirichlet problems for systems of variational elliptic PDEs defined on randomly perforated domains of Rn. Under the assumption that the perforations are small balls whose centres and radii are generated by a stationary short-range marked point process, we obtain in the critical-scaling limit an averaged nonlinear analogue of the extra term obtained in the classical work of Cioranescu and Murat. In analogy to the random setting recently introduced by Giunti, Hoefer, and Velazquez to study the Poisson equation, we only require that the random radii have finite (n-p)-moment, where 1