A parametric detection scheme for determenistic signals is obtained in a generalized observation model which contains non-additive noise. The model employed in this paper includes several special cases such as those describing purely-additive noise, multiplicative noise, and signal dependent noise and allows the consideration of deterministic and random signals. Locally optimum detectors for known deterministic signals in the model are derived and analyzed for performance. It is shown that the locally optimum detectors are interesting generalizations of those for the purely-additive noise model. Performance of the locally optimum detectors designed for the generalized observation model is compared to that of other common detectors.