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This paper addresses the problem of dense disparity estimation in networks of omnidirectional cameras. We propose to map omnidirectional images on the 2-sphere, and we perform disparity estimation directly on the sphere in order to preserve the geometry of images. We first perform rectification of the images in the spherical domain. Then we formulate a global energy minimization problem for the estimation of disparity on the sphere. We solve the optimization problem with a graph-cut algorithm, and we show that the proposed solution outperforms common methods based on block matching, for both synthetic scenes with varying complexity and complex natural scenes. Then, we propose a parallel implementation of the graph-cut algorithm that is able to perform dense depth estimation with an improved speed-up, which makes it suitable for realtime applications. Finally, we extend the spherical depth estimation framework to networks of multiple cameras, and we design two methods for dense depth estimation that are based respectively on disparity computation with pairs of images, or computation of inverse depth values. Both methods are shown to provide promising results towards depth estimation in networks of omnidirectional cameras. keywords: disparity estimation depth estimation omnidirectional imaging spherical images camera networks