  We investigate the dynamics of entanglement and nonlocality for multipartite
quantum systems under collective dephasing. Using an exact and computable
measure for genuine entanglement, we demonstrate the possibility of a non
trivial phenomenon of time-invariant entanglement for multipartite quantum
systems. We find that for four qubits, there exist quantum states, which are
changing continously nevertheless their genuine entanglement remains constant.
Based on our numerical results, we conjecture that there is no evidence of
time-invariant entanglement for quantum states of three qubits. We point out
that quantum states exhibiting time-invariant entanglement must live in both
decoherence free subspace and in the subspaces orthogonal to it. The previous
studies on this feature for two qubits can be recovered from our studies as a
special case. We also study the nonlocality of quantum states under collective
dephasing. We find that although genuine entanglement of quantum states may not
change, however their nonlocality changes. We discuss the possibility of finite
time end of genuine nonlocality.
