The　integrated　electricity-gas-heat　system　(IEGHS)　is　considered　as　an　important　carrier　to　promote　new　energy　consumption　and　achieve　the　goal　of　carbon　peaking　and　carbon　neutrality.　To　protect　the　private　information　of　electricity-gas-heat　networks,　this　paper　develops　a　distributed　optimal　scheduling　of　IEGHS　considering　dynamic　characteristics　of　networks.　First,　the　dynamic　models　of　networks　are　evaluated　to　explore　energy　storage　capacity.　Next,　the　distributed　optimization　model　of　electricity,　gas　and　heat　networks　are　established,　which　are　solved　by　a　generalized-alternating　direction　method　of　multiplier　(G-ADMM).　Finally,　the　joint　system　of　modified　IEEE　39　node　electricity　network,　15　node　heat　network　and　Belgium　20　node　gas　network　is　simulated,　which　proves　the　proposed　approach　can　fulfill　the　decentralized　autonomy　for　three　networks,　sufficiently　alleviate　the　fluctuation　of　loads　and　effectively　enhance　the　flexibility　and　reliability　of　IEGHS　operation.　©　2023　IEEE.