Abstract: To fully capitalize on the medium- and long-term storage benefits of hydrogen energy, a two-stage weekly optimization scheduling strategy for electric-hydrogen coupled microgrids is proposed, utilizing a scenario-based stochastic optimization model. Firstly, the mathematical models for the electric-hydrogen coupled equipment within the microgrid are developed. Secondly, aiming to minimize the weekly operation cost, the cycles of electric and hydrogen energy storage are set as weekly and daily, respectively, and the first-stage weekly scheduling model of the microgrid based on weekly prediction data is established. Then, to account for the uncertainty in wind power generation, typical scenarios of prediction errors are introduced. A day-ahead scheduling model considering uncertainty is constructed, aiming to minimize the sum of the daily expected operational cost and the deviation penalty for the two-stage hydrogen storage tank's state of charge. The final weekly operation scheme is determined through rolling optimization. Finally, case studies demonstrate that the proposed strategy effectively reduces the microgrid's operating costs and enhances energy utilization.