  We have developed quantitative description of quantum coherent oscillations
in the system of two coupled qubits in the presence of weak decoherence that in
general can be correlated between the two qubits. It is shown that in the
experimentally realized scheme of excitation of the oscillations, their
waveform is not very sensitive to the magnitude of decoherence correlations.
Modification of this scheme into potentially useful probe of the degree of
decoherence correlations at the two qubits is suggested.
