The conservation issues of pairwise quantum discord and entanglement of two qubits coupled to a two-mode vacuum cavity are investigated by considering the dipole^tipole interaction between two qubits. It is found that the sum of the square of the pairwise quantum discords and the sum of the square of the pairwise concurrences are both conserved in the strong dipole-dipole interaction limit. However, in the middle dipole-dipole and weak dipole-dipole interaction limits, the sum of the square of the pairwise concurrences is still conserved while the sum of the square of the pairwise discords is not. The crucial reason for this is that the quantum discords are not equivalent if the measurements are performed on different subsystems in a general situation. So it is very important for quantum computation depending on the quantum discord to select the target performed by the measurements.
