Mesh-based terrain representations provide accurate descriptions of a terrain, but fail in capturing its morphological structure. The morphology of a terrain is defined by its critical points and by the critical lines joining them, which form a so-called surface network. Because of the large size of current terrain data sets, a multi-resolution representation of the terrain morphology is crucial. Here, we address the problem of representing the morphology of a terrain at different resolutions. The basis of the multi-resolution terrain model, that we call a Multi-resolution Surface Network (MSN), is a generalization operator on a surface network, which produces a simplified representation incrementally. An MSN is combined with a multi-resolution mesh-based terrain model, which encompasses the terrain morphology at different resolutions. We show how variable-resolution representations can be extracted from an MSN, and we present also an implementation of an MSN in a compact encoding data structure.