  We study the dynamics of genuine multipartite entanglement for quantum
systems upto four qubits interacting with general collective dephasing process.
Using a computable entanglement monotone for multipartite systems, we observe
the feature of freezing dynamics of genuine entanglement for three and four
qubits entangled states. We compare the dynamics with that of random states and
find that most states exibit this feature. We then study the effects of
collective dephasing on genuine nonlocality and find out that although quantum
states remain genuinely entangled yet their genuine nonlocality is lost in a
finite time. We show the sensitivity of asymptotic states being genuinely
entangled by mixing white noise.
