In this paper, we introduce and investigate new concepts of L-weakly M-weakly demicompact operators. Let E be a Banach lattice. An operator T : ? is called demicompact, if for every norm bounded sequence (xn) in BE such that {xn Txn, n N} an compact subset E, have {xn, E. Additionally, disjoint ?xn ?Txn? 0, ?xn? 0. (resp. M-weakly) operators generalize known classes which are We also elaborate ...