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This paper presents a fully-decentralized peer-to-peer (P2P) electricity and gas market for retailers and prosumers with coupled energy units, considering the uncertainties of wholesale electricity market price and prosumers’ demand. The goal is to improve the overall economy of the proposed market while increasing its flexibility. In this market, the retailers are equipped with self-generation and energy storage units and can bilaterally negotiate for electricity and gas transactions with prosumers to maximize their profit. Furthermore, they can sell power to the upstream market in addition to prosumers. The prosumers have access to several retailers to supply their required electricity and gas and can freely provide their energy needs from every retailer, contributing to dynamicity in the proposed market. Given that they have an energy hub consisting of boiler units, combined heat and electricity (CHP) units, and electric pumps, they can switch their energy supply source from electricity to gas and vice versa. A robust possibilistic programming approach is applied to address the uncertainties. A fully-decentralized approach called the alternating direction method of multipliers (ADMM) is utilized to solve the presented decentralized robust problem. The proposed decentralized algorithm finds an optimum solution by establishing a smart balance between the average expected value, optimality robustness, and feasibility robustness. The feasibility and competitiveness of the proposed approach are evaluated through numerical studies on a distribution system with two retailers and three prosumers. The data analysis of the simulation results verifies the effectiveness of the proposed decentralized robust framework as well as the proposed decentralized solution. According to the maximum deviation, the expected optimal value in the robust case, the retailer’s profit has decreased by 12.1 percent, and the prosumers’ cost has increased by 27.4 percent due to the feasibility penalty term.