  Let $\mathcal{X}$ be a class of $R$-modules. In this paper, we investigate
\;$\mathcal{X}$-(f.g.)injective ((f.g.)projective) and
DG-$\mathcal{X}$-injective (projective) complexes which are generalizations of
injective (projective) and DG-injective (projective) complexes. We prove that
some known results can be extended to the class of
\;$\mathcal{X}$-(f.g.)injective ((f.g.)projective) and
DG-$\mathcal{X}$-injective (projective) complexes for this general settings.
