It is important to study the locally optimum detectors (LOD) both in theory and practice. In this paper a model and a criterion are proposed for the generalized LOD. On the basis of such criterion，the genevalized LOD structures are devived for detecting several typical signals in non-Gaussian noise，and the asymptotic relative efficiency (ARE) due to Pitman is used to evaluate their performance. Finally，numerical calculations are carried out for ARE of these LOD and some valuable conclusions are obtained.