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The synergistic operation of integrated electricity and natural gas systems (IEGS) in the presence of wind power necessitates a distributed optimization framework that ensures information privacy. However, incorporating wind power penetration leads to distributed optimization problems including uncertainty and unstable distributed algorithm's convergence. With the increasing proportion of wind power in IEGS, fluctuating wind power penetration highly affects the convergence of distributed optimization solutions, resulting in uncontrollable optimization time of the distributed algorithm. Accordingly, this paper investigates the impact of wind fluctuation and uncertainty on distributed IEGS optimization and proposes a novel fast distributed co-optimization framework. Specifically, an adaptive alternating direction method of multipliers (ADMM) is developed to accommodate wind fluctuation. Based on designed rules, the penalty parameter is updated in every step to maximize the gradient of the optimization objective. The experiments are conducted using real wind power generation data sourced from a wind farm in Australia and a classical IEGS framework composed of the IEEE 24-bus electricity system and a 12-node natural gas system. Compared to original ADMM and residual balancing ADMM, the proposed framework achieves an average reduction of 0–91.4% in the number of iterative steps for multiple solution iterations across various scenarios, with a corresponding decrease in the standard deviation by 13.8%–93.0%. • Fast and stable convergence of IEGS distributed optimization problem. • ADMM with an adaptive penalty parameter guarantees the convergence. • Update rate further improves the sensibility of the penalty parameter. • Mean value and standard deviation of running iterations significantly decrease. [ABSTRACT FROM AUTHOR]