We generalize the two-scale convergence concept which was introduced by Nguet-seng [29]. In this generalized method we use test functions which does not have to be periodic. We also prove some compactness results which we use in a homogeniza-tion procedure for linear and non-linear parabolic equations, in perforated domains, with coefficients oscillating in both their space and time variables. Further, we prove some corrector-type results for the linear case.