In this paper, the problem of locally optimum detection of weak pulse signals innarrow-band non-Gaussian noise is discussed. A generalized model is proposed for locally optimumdetectors (LOD) and the corresponding physical meaning is explained. On the basis of this generalized model, the LOD structures are derived for detecting both coherent- and incoherent-pulse signals in narrow-band non-Gaussian noise. The asymptotic relative efficiency (ARE) due to Pitman is used to evaluate the performance of these LODs. Finally, numerical calculations are carried out for the AREs of these LODs and some valuable results are obtained.