The　electricity-hydrogen　coupling　system　(EHCS)　aims　to　enhance　the　diversification　of　energy　use　and　reduce　carbon　emissions.　However,　fraudulent　behaviors　within　the　market　environment　can　impede　the　energy　sharing　within　the　EHCS.　This　paper　establishes　a　peer-to-peer　(P2P)　energy　trading　framework　for　EHCSs　that　accounts　for　fraudulent　behaviors　into　account.　First,　a　cooperative　operational　framework　for　EHCS　is　established,　upon　which　an　internal　device　model　for　EHCSs　is　subsequently　constructed.　To　optimize　energy　trading,　carbon　trading　is　introduced,　and　a　Nash　bargaining　problem　is　formulated,　subsequently　decomposed　into　two　subproblems.　To　safeguard　privacy,　the　alternating　direction　method　of　multipliers　(ADMM)　is　employed　to　solve　these　subproblems.　Furthermore,　to　ensure　stable　cooperation　and　maximize　trading　benefits,　a　fraudulent　behaviors　equilibrium　mechanism　is　proposed.　The　results　of　case　studies　show　that　the　proposed　P2P　trading　mechanism　can　achieve　fraudulent　behaviors　equilibrium,　reduce　energy　waste,　and　enhance　the　economic　benefits　of　the　alliance.