Let n and m be infinite cardinals with n ≤ m and n be a regular cardinal. We prove certain implications of [ n , m ] -strongly paracompact, [ n , m ] -paracompact and [ n , m ] -metacompact spaces. Let X be [ n , ∞ ] -compact and Y be a [ n , m ] -paracompact (resp. [ n , ∞ ] -paracompact), P n -space (resp. w P n -space). If m = ∑ k < n m k we prove that X × Y is [ n , m ] -paracompact (resp. [ n , ∞ ] -paracompact