This paper is a continuation of [Erguang YANG. On some generalized countably compact spaces. J. Math. Res. Appl., 2019, {\bf 39}(5): 540--550] in which characterizations of some generalized countably compact spaces such as quasi-$\gamma$ spaces, quasi-Nagata spaces, $wN$-spaces and $wM$-spaces in terms of real-valued functions were obtained. In this paper, we shall present some other forms of characterizations of the spaces mentioned above.
