The article under review extends the notion of strongly Gorenstein flat modules first to strongly Gorenstein flat complexes (abbreviated as $SG$-flat complexes) and then to $n$-$SG$-flat complexes. The Gorenstein flat complexes are those which are a kernel for an exact sequence of complexes of flat modules where the exact sequence of complexes remains exact as a sequence of complexes upon tensoring with any injective complex. Strongly Gorenstein complexes require that every complex within the exact sequence is identical and that every map in the sequence is identical. The present paper contains generalizations of results from [D. Bennis and N. Mahdou, J. Pure Appl. Algebra {\bf 210} (2007), no.~2, 437--445; MR2320007] and [X.~Y. Yang and Z.~K. Liu, J. Algebra {\bf 320} (2008), no.~7, 2659--2674; MR2441993], two papers with the same title of ``Strongly Gorenstein projective, injective and flat modules''. Among these is the characterization of $SG$-flat complexes as those $ G $ for which there is a short exact sequence $ 0 \to G \to F \to G \to 0 $ with $ F $ being a flat complex and with $ \roman{Tor}_1(I, G) = 0 $ for any injective complex $ I $ (of right modules). Extending the short exact sequence to a longer exact sequence with terms $ F_n, \ldots, F_1 $ in place of $ F $ gives the notion of $ n $-$ SG $-flat complex. The paper then generalizes results from [G. Zhao and Z.~Y. Huang, Comm. Algebra {\bf 39} (2011), no.~8, 3044--3062; MR2834145]. The organization and writing style of the paper are clear, with the caveat that readers should be aware that the underlined notation from §2 is not fully explained with regard to $ \roman{Hom} $ [see X.~Y. Yang and Z.~K. Liu, Comm. Algebra {\bf 39} (2011), no.~5, 1705--1721; MR2821502].