We investigate the effects of fluxon cotunneling and quantum Coulomb drag in a system of two small Josephson junctions coupled by means of mutual capacitance $C_m$. Depending on the value of $C_m$ we identify three different regimes of strong, intermediate, and weak coupling. Focusing our attention on the last two regimes we develop a perturbation theory in the interaction and explicitly derive fluxon cotunneling amplitudes at sufficiently small mutual capacitance values. We demonstrate that the Coulomb drag effect survives at any nonzero $C_m$ and evaluate the nonlocal voltage response that is in general determined by a trade-off between two different cotunneling processes. Our predictions can be straightforwardly generalized to bilinear Josephson chains and directly verified in future experiments.

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• Instantons
• Josephson effect
• Phase slips
• Josephson junctions
• Path-integral methods