Some pelagic decapod crustaceans have long trailing antennal `flagella', the distal parts of which are heavily setosed. In these distal parts some setae form tubes known to contain mechanoreceptors and so resemble the lateral lines of many common fishes. We have studied some of the mechanical properties of these specialized flagella from animals of the families Sergestidae and Penaeidae. Both proximal and distal parts of the flagella are flexible at right angles to their lengths but behave like rigid bodies longitudinally. This means that when the animal is exposed to vibrations in the surrounding sea water the distal parts behave, at all frequencies greater than about 1 Hz, as if they are, in the planes perpendicular to the axes of the proximal parts, mechanically independent of the animal's body. The way in which the ratio of the displacements of the mechanoreceptors in the distal parts of the flagellum and the displacements of the sea water outside the flagellum changes with frequency was found. This resembles that found for some fish lateral lines. From these results it seems that these crustaceans have two `lateral lines' widely spaced from the animal's body and mechanically independent of the body. For such a system the patterns of excitation of the mechano-receptors of the flagella will change in an even more dramatic way with change in position of an external source of vibration than will be the case for fish lateral lines. We have calculated such changes in pattern for a few simple spatial dispositions of a vibrating source and a crustacean of this kind.