We present a hybrid 3D-2D algorithm for stabilizing 360◦ video using a deformable rotation motion model. Our algorithm uses 3D analysis to estimate the rotation between key frames that are appropriately spaced such that the right amount of motion has occurred to make that operation reliable. For the remaining frames, it uses 2D optimization to maximize the visual smoothness of feature point trajectories. A new low-dimensional flexible deformed rotation motion model enables handling small translational jitter, parallax, lens deformation, and rolling shutter wobble. Our 3D-2D architecture achieves better robustness, speed, and smoothing ability than either pure 2D or 3D methods can provide. Stabilizing a video with our method takes less time than playing it at normal speed. The results are sufficiently smooth to be played back at high speed-up factors; for this purpose we present a simple 360◦ hyperlapse algorithm that remaps the video frame time stamps to balance the apparent camera velocity.