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It has long been known that the statistical properties of acoustic echoes from individual fish can have non-Rayleigh characteristics. The statistical properties of echoes from zooplankton are generally less understood. In this study, echoes from individual fish and zooplankton from a series of laboratory measurements from the past decade are investigated. In the experiments, acoustic echoes from various individual organisms were measured over a wide range of frequencies and orientations, typically in 1°-3° increments. In the analysis in this paper, the echoes from most of those measurements are grouped according to ranges of orientation, which correspond to typical orientation distributions of these organisms in the natural ocean environment. This grouping provides a distribution of echo values for each range of orientation. This approach, in essence, emulates a field experiment whereby distributions of echoes would be recorded for different distributions of orientations of the organisms. For both the fish and zooplankton data, there are conditions under which the echoes are strongly non-Rayleigh distributed. In some cases, the distribution is quantitatively connected to the physics of the scattering process while, in other cases, the connection is described qualitatively. Exploitation of the animal-specific statistics for classification purposes is suggested.