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We prove that, for any $n \geq 2$, the classes of $\rm{FP}_{n}$-injectivemodules and of $\rm{FP}_n$-flat modules are both covering and preenvelopingover any ring $R$. This includes the case of $\rm{FP}_{\infty}$-injective and$\rm{FP}_{\infty}$-flat modules (i.e. absolutely clean and, respectively, levelmodules). Then we consider a generalization of the class of (strongly)Gorenstein flat modules - the (strongly) Gorenstein AC-flat modules (cycles ofexact complexes of flat modules that remain exact when tensored with anyabsolutely clean module). We prove that some of the properties of Gorensteinflat modules extend to the class of Gorenstein AC-flat modules; for example weshow that this class is precovering over any ring $R$. We also show that (as inthe case of Gorenstein flat modules) every Gorenstein AC-flat module is adirect summand of a strongly Gorenstein AC-flat module. When $R$ is such thatthe class of Gorenstein AC-flat modules is closed under extensions, theconverse is also true. We also prove that if the class of Gorenstein AC-flatmodules is closed under extensions, then this class of modules is covering.

$\rm{FP}_{n}$-injective and $\rm{FP}_{n}$-flat covers and preenvelopes, and Gorenstein AC-flat covers