This paper deals with fault diagnosis of timed discrete event systems (TDESs), using a nondeterministic model named labeled time Petri net (LTPN). Thanks to a skillful splitting of time intervals assigned to the LTPN transitions, analyzing diagnosability in such a timed context can be performed using techniques from the untimed context. Moreover, a deterministic structure called augmented state class set graph (ASG) is built on the fly, for both analyzing (∆-)diagnosability and deriving an online diagnoser.