A parallelization of the algorithm of Golumbic for recognizing comparability graphs is proposed for the concurrent parallel random access machine (CRCW PRAM). Parallel algorithms for finding a transitive orientation and the modular decomposition of any undirected graph are deduced from an extension of the theory of Golumbic toward modular decomposition. The algorithms for recognizing and transitively orienting comparability graphs run in O(log n) time using d m processors and the modular decomposition algorithm runs in O(log n) time using n^3 processors (n, m and d respectively denote the number of vertices, the number of edges and the maximal degree of the undirected input graph).