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We study Josephson-like junctions formed by materials with antiferromagnetic (AF) order parameters. As an antiferromagnet, we consider a two-band material in which a spin density wave (SDW) arises. The spin current j sub(Sp) in AF/F/AF junctions with a ballistic ferromagnetic layer and in tunnel AF/I/AF junctions is calculated. It depends on the angle between the magnetization vectors in the AF leads in the same way as the Josephson current depends on the phase difference of the superconducting order parameters in S/I/S tunnel junctions. We also calculate the dependence of j sub(Sp) on the deviation from the ideal nesting in the AF/I/AF junctions. The spin current is maximal in the insulating phase of the AF and decreases in the metallic phase. It turns to zero at the Neel point when the amplitude of the SDW is zero and changes sign for certain values of the detuning parameter.