Operational optimization problems of multi-energy systems have to be solved repeatedly, e.g., to react to changing energy prices. Thus, operational optimization problems should compute fast. The computation time of operational optimization problems is, therefore, often reduced by the Rolling-Horizon method. The Rolling-Horizon method decomposes the original optimization problem heuristically into smaller subproblems. Each subproblem optimizes only the next few time steps of the whole time series. While reducing computation time, the Rolling-Horizon solutions are, in general, suboptimal for the original problem. For example, suboptimal decisions arise for start-ups and shut-downs of components in a multienergy system, if the subproblems are too short to contain sufficient information about future energy prices. Longer subproblems increase solution quality, but also computation time.To resolve this trade-off between solution quality and computation time, we propose the Adaptive-Rolling-Horizon approach. Adaptive Rolling Horizon adjusts the size of each subproblem based on the energy-price predictions and the current system state. Adaptive Rolling Horizon aims to keep the subproblems as short as possible to minimize computation time, but as long as necessary to resolve optimal decisions about start-ups and shut-downs. In a real-world case study, Adaptive Rolling Horizon reduces the computation time by up to two orders of magnitude while achieving a near-optimal solution. At the same time, Adaptive Rolling Horizon can improve the solution quality by more than 15 % compared to common Rolling Horizon. The results show that Adaptive Rolling Horizon can significantly accelerate the operational optimization of multi-energy systems while retaining high solution quality.