The authors introduced the concept of occasionally weakly compatible maps in [Acta Math. Sin., Engl. Ser. 24, No. 5, 867–876 (2008; Zbl 1175.41026
)]. Here, they prove that a pair of selfmaps of a discrete metric space is weakly compatible iff it is weakly commuting, provided that the set of their coincidence points is nonempty. A suitable example shows that this remark is not extensible to a pair of occasionally weakly compatible maps, even if defined over a discrete metric space.