When orignal signals are contaminated by both additive and signal-dependent noise components, the test statistics of locally optimum detector are obtained for detection of weak composite signals based on the generalized Neyman-Pearson lemma. In order to consider the non-additive noise as well as purely-additive noise, a generalized observation model is used in this paper. The locally optimum detector test statisics are derived for all different cases according to the relative strengths of the known signal, random signal, and signal-dependent noise components. Schematic diagrams of the structures of the locally optimum detector are also included. The finite sample-size performance characteristics of the locally optimum detector are compared with those of other common detectors.