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Recently, Costa [4] introduced the concept of n-coherent rings. In this note we shall give some further properties of n-coherent rings. Let R be a ring and na nonnegative integer. Following [4], a left R-module M is called n-presented if it has a finite n-presentation, ie, there is an exact sequence Fn+ F,,-l-+.-+ Fl+ Fo+ M+ 0 in which every F, is a finitely generated free left R-module. A ring R is said to be left n-coherent if every n-presented left R-module is (n+ 1)-presented. It is easily seen that R is left 0-coherent (resp. 1-coherent) if and only if R is left Noetherian (resp. coherent)(see [4, 6, 131). Coherent rings have been studied by many authors (see, eg,[2, 5, 6, 11, 131). The object of this paper is to characterize left n-coherent rings for a fixed positive integer n. We give various equivalent conditions for a ring to be left tz-coherent. It is shown that there are many similarities between coherent rings and n-coherent rings. For …