We address the problem of designing compact data structures for encoding a Triangulated IrreguIar Network (TIN) as a sequential bltstrearn. In particular, we study the problem of compressing connectivity, i.e., the information describing the topological structure of the TIN and we propose two new compression methods which have different purposes. The goal of the first method is to minimize the number of bits needed to encode connectivity information it encodes each wrtaY once, and requires two lits of connectivity information for each edge of a TIN. We present efficient algorithms for coding and decoding the corresponding bitstream and show some practical evaluation of the method. The second method compresses a TIN at progressive levels of detail and is based on a strategy which iteratively removes a vertex from a TIN according to an error-based criterion. Encoding and decoding algorithms are presented and compared with other approaches to progressive compression.