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Hierarchical terrain models describe a topographic surface at di erent levels of detail, providing a multiresolution representation as well as a data compression mechanism. In this paper, we consider the problem of computing the visibility map, with respect to a xed viewpoint, on a hierarchical triangle-based terrain model. This problem presents two aspects: the extraction of a visibility map at a given resolution, and the update of such map as the resolution increases. In particular, we focus on the dynamical update of the visibility map when the terrain resolution is increased by expanding a subset of faces into ner triangular tesselations. We propose a randomized algorithm for maintaining the visibility map under insertions and deletions of triangles (terrain faces). The expected space complexity of the algorithm is equal to ( ) (i.e., worst-case optimal), and the expected update time for both inserting and deleting a randomly selected triangle is equal to ( log ).