Cofiniteness of generalized local cohomology modules

Let Formula: see text be an ideal of a commutative noetherian ring Formula: see text and Formula: see text two Formula: see text-modules with Formula: see text finitely generated. It is shown that if either Formula: see text is an Formula: see text-cofinite module of dimension Formula: see text for all Formula: see text, or Formula: see text is a principal ideal and Formula: see text is finitely generated for all Formula: see text, or Formula: see text is finitely generated and Formula: see text for all Formula: see text, then the Formula: see text-module Formula: see text is Formula: see text-cofinite for all Formula: see text.