Abstract: The discrete-time detection of narrowband coherent and incoherent pulse train signals in narrowband non-Gaussian noise is investigated. The structures of local-opti-mum(LO) detector are developed and found to be in the form of incorporating a local-optimum zero-memory nonlinearity (LOZNL) into the Neyman-Pearson optimum detector for narrowband Gaussian noise. Many practical detectors belong to the same class of structures of the LO detector. The expressions for the efficacies of the detectors are derived. In particular, Weibull and log-normal noise models are considered. The LOZNLs and the efficacies of the detectors are given, and the numerical results are presented graphically. It is shown that, in the sense of Pitman asymptotic relative efficiency (ARE), the asymptotic performance of many detectors whose nonlinearity can more effectively suppress the tail of the noise envelope distribution is apparently better than that of the Neyman-Pearson optimum detector for narrowband Gaussian noise.