For a given ideal I of a Noetherian ring R and an arbitrary integer ${kappa}{geq}-1$, we apply the concept of ${kappa}$-regular sequences and the notion of ${kappa}$-depth to give some results on modules called ${kappa}$-Cohen Macaulay modules, which in local case, is exactly the ${kappa}$-modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any ${kappa}$-regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any ${kappa}$-regular sequence is at most ${kappa}$. Therefore homology modules of the Koszul complex with respect to any filter regular sequence has finite length.