Summary: We prove that the \(n\)th pure braid group of a nonorientable surface (closed or with boundary, but different from \(\mathbb{RP}^{2}\)) is residually 2-finite. Consequently, this group is residually nilpotent. The key ingredient in the closed case is the notion of \(p\)-almost direct product, which is a generalization of the notion of almost direct product. We also prove some results on lower central series and augmentation ideals of \(p\)-almost direct products.