The main objective is showing a variant of resolution theorem of connective Waldhausen K-theory in suitable situations. We construct two sequences of subcategories, one is consisting of finitely generated symmetric module spectra which satisfy the condition of the resolution theorem and the other is consisting of the corresponding ∞-subcategories of certain finitely generated module spectra. As an application, we construct a sequence of subcategories consisting of certain DG-modules satisfying the condition of a resolution theorem.

Mathematics Subject Classification. Primary 18E99; Secondary 19D10.