The learning approach to fault diagnosis provides a methodology for designing monitoring architectures which can he used for detection, identification and accommodation of failures in dynamical systems. This paper considers the issues of detectability conditions and detection time in a nonlinear fault diagnosis scheme based on the learning approach. First, conditions are derived to characterize the range of detectable faults. Then, nonconservative upper bounds are computed for the detection time of incipient and abrupt faults. It is shown that the detection time bound decreases monotonically as the values of certain design parameters increase. The theoretical results are illustrated by a simulation example of a second-order system.