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In this paper, we introduce the tube surfaces in pseudo-Galilean 3-space. We classify the tube surfaces into two types according to the spine curve which generates the tube surface in pseudo-Galilean space. Moreover, we show that both types of tube surfaces are spacelike surfaces. Then, we begin to study the local geometry of the tube surfaces. We obtain the first and second fundamental forms of the tube surfaces. In addition, we investigate the Gauss and mean curvatures of the tube surfaces in pseudo-Galilean space.