This paper presents an efficient algorithm for enumerating all minimal a-b separators separating given non-adjacent vertices a and b in an undirected connected simple graph G = (V,E). Our algorithm requires O(n3R,b) time, which improves the known result of 0(n4R,b) time for solving this problem, where IV1 = n and R,b is the number of minimal a-b separators. The algorithm can be generalized for enumerating all minimal A-B separators that separate non-adjacent vertex sets A,B c V, and it requires O(n2(n -no -nB)RAB) time in this case, where IDA = IAl, rz~ = lB1 and RAB is the number of all minimal A-B separators. Using the algorithm above as a routine, an efficient algorithm for enumerating all minimal separators of G separating G into at least two connected components is constructed. The algorithm runs in time 0(n3Ri + n4Rz), which improves the known result of O(#Rz) time, where Rz is the number of all minimal separators of G and RZ6Rg = Cl<ifj<n,(q,o,)@ R,,, <(n(n -1)/2 ~ m)Rz. Efficient parallelization of these algorithms is also discussed. It is shown that the first algorithm requires at most O((n/logn)Rab) time and the second one runs in time O((n/log rt)Ri +n log ~Rz) on a CREW PRAM with 0(n3 ) processors.