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Let (R,m) be a Noetherian local ring and M a finitely generated R-module with dimM=d. Let i⩾0 be an integer. Following M. Brodmann and R.Y. Sharp (2002) [BS1], the i-th pseudo support of M is the set of all prime ideals p of R such that [Formula: see text] . In this paper, we study the pseudo supports and the non-Cohen–Macaulay locus of M in connections with the catenarity of the ring R/Ann_RM, the Serre conditions on M, and the unmixedness of the local rings R/p for certain prime ideals p in Supp_R(M).