Quantum correlations are considered analytically in a model that contains two coupled superconducting charge qubits sharing a large Josephson junction. Dynamical properties for the reduced two-qubit state are addressed in the quantum evolution when the coupling between the field and the qubits is either constant or time-dependent. In the latter case, adiabatic and nonergodic features are present for extremely low and fast evolutions, respectively. Finally, the case where the coupling drops to zero is also considered.