The detection of underwater acoustic signals by simple correlation receivers in the presence of general classes of additive non-normal, as well as normal background noise, is studied from the viewpoint of statistical decision theory. Performance is measured in terms of average risk the probabilities of decision error are found for deterministic and stochastic signals in the threshold situation of large samples and independent sampling on the observation interval. As such, these error probabilities are upper bounds on the values that would be obtained with continuous sampling on the same interval. Non-normal noise may either worsen or better detection vis-a-vis normal noise backgrounds, depending on the positive or negative values of the abnormality factors, which are the pertinent measures here of the departure from normality of the background noise. Effective detection requires uniform post-multiplier weighting of the sampled data, and a positive value of the signals crosscorrelation or coherent detection can be achieved with sufficiently strong injected signals, to operate independently of the particular noise statistics.