This chapter is devoted to the higher-dimensional case. It is shown that the limit of holomorphic G-convergence for divergence form problems with highly oscillatory, periodic, sign-changing coefficients depends on whether the integral mean of the inverse of the coefficients or the integral mean of the coefficients itself vanishes. For example, vanishing integral mean of the inverse yields a limit with spectrum on the entire complex plain. Non-vanishing integral mean of the inverse together with vanishing integral mean yields a nonlocal equation of 4th order in the limit. Examples are provided.