Abstract: N-strongly Gorenstein FP-injective modules are investigated, that M is a n-strongly Gorenstein FP-injective module if and only if N-M is a n-strongly Gorenstein FP-injective module for any projective module N over left coherent rings which are right IF rings is proved, and that M is a n-strongly Gorenstein FP-module if and only if M is a nstrongly Gorenstein flat module over left and right IF rings is proved.

Key words: IF ring, strongly Gorenstein FP-injective module, n-strongly Gorenstein FP-injective module, coherent ring