Fault diagnosis of processors has played an essential role when evaluating the reliability of multiprocessor systems. In many novel multiprocessor systems, their diagnosability has been extensively explored. Conditional diagnosability is a useful measure for evaluating diagnosability by adding a further condition that all neighbors of every node in the system do not fail at the same time. In this paper, we study the conditional diagnosability of n-dimensional alternating group networks ANn under the PMC model, and obtain the results tc(AN₄) = 5, and tc(ANn) = 6n - 17 for n > 5. In addition, for the isomorphism property between AN_n and S_n,k with k = n-2, namely (n, n - 2)-star graphs S_n,n-2, the above results can be extended to S_n,n-2, and we have tc(S_4,2) = 5 and tc(S_n,n-2) = 6n - 17 for n > 5. It is worth noting that the conditional diagnosability is about six times the degree of ANn andS_n,n-2, which is very different from general networks with a multiple of four.