The exchanged hypercube EH(s, t)(where s≥1 and t ≥1) is obtained by systematically reducing links from a regular hypercube Qs+t+1. One-step diagnosis of exchanged hypercubes which involves only one testing phase during which processors test each other is discussed. The diagnosabilities of exchanged hypercubes are studied by using the pessimistic one-step diagnosis strategy under two kinds of diagnosis models: the PMC model and the M M*model. The main results presented here are the two proofs that the degree of diagnosability of the EH(s, t) under pessimistic one-step t1/t1 fault diagnosis strategy is 2s where1≤s≤t(respectively, 2t, where 1≤t≤s) based on the PMC model and that it is also 2s where 1≤s≤t(respectively, 2t,where 1≤t≤s) based on the M M*model. The exchanged hypercube EH (s, t) (where s ≧ 1 and t ≧ 1) is obtained by systematically reducing links from a regular hypercube Qs + t + 1. One-step diagnosis of exchanged hypercubes which involves only one testing phase during which The diagnosabilities of exchanged hypercubes are studied by using the pessimistic one-step diagnosis strategy under two kinds of diagnosis models: the PMC model and the MM * model. The main results presented here are the two proofs that the degree of diagnosis of the EH (s, t) under pessimistic one-step t1 / t1 fault diagnosis strategy is 2s where1≤s≤t (respectively, 2t, where 1≤t≤s) based on the PMC model and that it is also 2s where 1 ≦ s ≦ t (respectively, 2t, where 1 ≦ t ≦ s) based on the MM * model.