A generalization of the notion of depth of an ideal on a module is introduced by applying the concept of local cohomology modules with respect to a pair of ideals . The concept of (I; J)- Cohen{Macaulay modules is also introduced as a generalization of the concept of Cohen{Macaulay modules . This kind of modules is di erent from the Cohen{Macaulay modules, as shown in an example. Also an Artinian result is given for such modules.
