Using a generalized observation model, in which one can express the effects of non-additive noise such as signal-dependent noise and multiplicative noise in addition to purely-additive noise, the problem of weak random-signal detection is investigated. It is shown that the test statistics of locally optimum detectors for detection of weak random signals in signal-dependent noise model are interesting extensions of those in purely-additive noise model. This result is a complement to the result for weak random-signal detction in multiplicative noise model.