  Let $R$ be any associative ring with unity and $\mathcal{X}$ be a class of
$R$-modules of closed under direct sum (and summands) and with extension
closed. We prove that every complex has an $C(\mathcal{X^{*}})$-cover
($C(\mathcal{X^{*}})$-envelope) if every module has an $\mathcal{X}$-cover
($\mathcal{X}$-envelope) where $C(\mathcal{X^{*}})$ is the class of complexes
of modules in $\mathcal{X}$ such that it is closed under direct and inverse
limit.
