tAn analytical solution of the master equation for two qubits-field system, in the dispersive regime, areinvestigated. The qubits are initially in Werner states and the field in coherent state. Under the influence ofthe damping, the geometric measure of quantum discord (GMQD) and the measurement-induced nonlo-cality (MIN) are investigated. GMQD and MIN are compared and illustrated their different characteristics.It is found that under the influence of damping the phenomenon of the death occurs for GMQD, but thisphenomenon does not occur for MIN even when the damping parameter is high. The initial conditionsfor the qubits play an important role in the phenomenon of collapses and revivals for GMQD and MIN.