Multi-frame super-resolution is the process of recovering a high resolution image or video from a set of captured low resolution images. Super-resolution approaches have been largely explored in 2-D imaging. However, their extension to depth videos is not straightforward due to the textureless nature of depth data, and to their high frequency contents coupled with fast motion artifacts. Recently, few attempts have been introduced where only the super-resolution of static depth scenes has been addressed. In this work, we propose to enhance the resolution of dynamic depth videos with non-rigidly moving objects. The proposed approach is based on a new data model that uses densely upsampled, and cumulatively registered versions of the observed low resolution depth frames. We show the impact of upsampling in increasing the sub-pixel accuracy and reducing the rounding error of the motion vectors. Furthermore, with the proposed cumulative motion estimation, a high registration accuracy is achieved between non-successive upsampled frames with relative large motions. A statistical performance analysis is derived in terms of mean square error explaining the effect of the number of observed frames and the effect of the super-resolution factor at a given noise level. We evaluate the accuracy of the proposed algorithm theoretically and experimentally as function of the SR factor, and the level of noise contamination. Experimental results on both real and synthetic data show the effectiveness of the proposed algorithm on dynamic depth videos as compared to state-of-art methods.