Cut trees are a compact representation of the edge-connectivity between every pair of vertices of an undirected graph, and have a large number of applications. In this work a parallel version of the well known Gomory-Hu cut tree algorithm is presented. The parallel strategy is based on the master/slave model. The strategy is optimistic in the sense that the master process manipulates the tree being constructed and the slaves solve minimum s-t-cuts independently. Another version is proposed that employs a heuristic that enumerates all (up to a limit) of the minimum s-t-cuts in order to choose the most balanced one. The algorithm was implemented and extensive experimental results are presented, including a comparison with Gusfieldâs cut tree algorithm. Parallel versions of these algorithms have achieved significant speedups on real and synthetic graphs. We discuss the trade-offs between the two alternatives, each of which presents better results given the characteristics of the input graph. In particular, the existence of balanced cuts clearly gives an advantage to Gomory-Huâsalgorithm.