  The conditions are established for nullity of quantum discord for mixed
states of a general two-qubit system whose dynamical behaviour is given by an
X-state form density matrix. It is found that quantum discord can vanish at a
finite time even in the presence of correlations between qubits. The degeneracy
of the populations of the combined states of the qubits and the multi-qubit
quantum coherences are shown to be responsible for vanishing of the discord. We
illustrate our considerations by examining the coherent-state Tavis-Cummings
model in which two qubits interact dispersively with the cavity field. The
disappearance of the discord is shown to be dependent on the initial atomic
conditions that it may occur at a discrete instance or periodically at discrete
instances redistributed over whole range of the evolution time. The nullity of
the discord is interpreted as resulting from equal preparation of the spin
anti-correlated and spin correlated product states in superposition~states.
