In　microgrid　(MG)　systems,　traditional　centralised　energy　trading　models　can　lead　to　issues　such　as　low　energy　efficiency　due　to　unstable　energy　supply　and　lack　of　flexibility.　Peer-to-peer　(P2P)　trading　models　have　been　widely　used　due　to　their　advantages　in　promoting　the　sustainable　development　of　renewable　energy　and　reducing　energy　trading　costs.　However,　P2P　multi-energy　trading　requires　mutual　agreements　between　two　microgrids　(MGs),　and　the　uncertainties　of　renewable　energy　and　load　affects　energy　supply　security.　To　address　these　issues,　this　article　proposed　a　distributed　robust　operation　strategy　based　on　P2P　multi-energy　trading　for　multi-microgrid　(MMG)　systems.　Firstly,　a　two-stage　robust　optimisation　(TRO)　method　was　adopted　to　consider　the　uncertainties　of　P2P　multi-energy　trading　between　MGs,　which　reduced　the　conservatism　of　robust　optimisation　(RO).　Secondly,　a　TRO　model　for　P2P　multi-energy　trading　among　MGs　was　established　based　on　the　Nash　bargaining　theory,　where　each　MG　negotiates　with　others　based　on　their　energy　contributions　in　the　cooperation.　Additionally,　a　distributed　algorithm　was　used　to　protect　the　privacy　of　each　MG.　Finally,　the　simulation　results　based　on　three MGs　showed　that　the　proposed　approach　can　achieve　a　fair　distribution　of　cooperative　interests　and　effectively　promote　cooperation　among　MGs.　©　2023　The　Authors.　IET　Energy　Systems　Integration　published　by　John　Wiley　&　Sons　Ltd　on　behalf　of　The　Institution　of　Engineering　and　Technology　and　Tianjin　University.