  We propose two classes of the generalized concurrence vectors of the
multipartite systems consisting of qubits. Making use of them, we are able to,
respectively, describe and quantify GHZ-class and W-class entanglement both in
total and between arbitrary two partite in the multipartite system consisting
of qubits. In the case of pure state of three qubits that one partite is
separable, it is shown to exactly back to the usual Wootters' concurrence after
introduce a whole concurrence vector. In principle, our method is applicable to
any $N$-partite systems consisting of $N$ qubits.
