Abstract. We describe a new method for the exploration of evolutionary relations between protein structures. The approach is based on the ESSM algorithm for detecting structural mutations, the output of which is then used for construction of fold space graphs. Fold space graphs can be regarded as a convenient tool for visualization and analysis of evolutionary relationships between protein structures, providing more information than traditional phylogenetic approaches. We have applied the method for analysis of evolutionary relations between CATH protein domains. The experiments allowed us to obtain estimates of the distribution of probabilities for different types of fold mutations, detect several chains of evolutionary related protein domains as well as to explore the most probable -sheet extension scenarios.