The dynamical evolution of nonclassical correlation in interacting qubits is investigated under the correlated dissipative environments for two classes of initial states.If the correlated decay rate equals the independent decay rate,there will be stationary nonclassical correlation between the qubits prepared initially in some separable states.When the correlated decay rate is different from the independent decay rate,the nonclassical correlation between the qubits eventually decays to zero for a certain class of initial states.Quantum entanglement is one of the most remarkable features of quantum mechanics and it plays a central role in quantum information and communication theory.There exists,however,nonclassical correlation,which is more general and more fundamental than entanglement in the sense that separable mixed states can have nonclassical correlation.Moreover,nonclassical correlation other than entanglement can be responsible for the quantum computational efficiency of deterministic quantum computation with one pure qubit.[1,2] Nonclassical correlation has also been used in other physical contexts,such as improving the efficiency of quantum Caot engines,[3] quantum phase transition and Grover search processes.[4-6]In these contexts,nonclassical correlation could be a new resource for quantum computation.Quantum discord,the most popular measure of such correlations,was introduced by Olliver and Zurek.[7]