We investigate the decoherence and dephasing of two coupled Josephson qubits. With the interaction between the qubits being generated by current–current correlations, two different situations in which the qubits are coupled to the same bath, or to two independent baths, are considered. Upon focussing on dissipation being caused by the fluctuations of voltage sources, the relaxation and dephasing rates are explicitly evaluated. Analytical and numerical results for the coupled qubits dynamics are provided.