We consider a family of non-convex integral functionals 1/h(2) integral(Omega) W(x/epsilon, Id +h del g(x)) dx, g is an element of W-1,W-p (Omega; R-n) where W is a Carath,odory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the I"-limits corresponding to linearization (h -> 0) and homogenization (epsilon -> 0) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W.