This paper presents a method for stabilizing both cylindrical and spherical panorama videos with a 360-degree field of view. We observe that rotation needs to be extremely smooth for 360 videos to maintain global motion coherency and avoid wobbling. Our method decouples the rotation from other motions and applies different strategies for smoothing them. The proposed approach is 2.5D as it estimates 3D rotations without involving 3D structure-from-motion methods. Therefore, it is more robust and can be performed in an incremental way. Experiments show that our method is effective in making steady 360 cylindrical/spherical videos.