Hierarchical terrain models provide a multiresolution description of a topographic surface based on a nested partition of the domain. The tree-like structure of these models is an effective support to processing spatial operations. In this paper, we consider visibility computations on hierarchical terrain models based on triangular subdivisions, called Hierarchical Triangulated Irregular Networks (HTINs). We address two basic problems in visibility computation, namely determining the visibility of a query object, and computing the viewshed of a given viewpoint. We propose algorithms for performing such operations on an HTIN at variable resolution. A general drawback of hierarchical models is in the inconsistency of representations at variable resolution obtained from them, since vertical gaps may occur at edges where different resolutions meet. The algorithms proposed here avoid this undesired effect. A related, but independent, contribution of this paper is also a new algorithm for extracting a consistent terrain representation at variable resolution from an HTIN.