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One-dimensional (1D) ferrimagnetism has recently been reported in ordered bimetallic compounds. Actually, such a behavior is not exclusive of this type of system. Ferrimagnetism can also occur in homometallic chains formed by alternating sites, or by discrete species containing an odd number of interacting metal ions. We report in this paper several examples of bimetallic or homometallic chains featuring 1D ferrimagnetism. We will also discuss the conditions for the occurrence of a long-range ferrimagnetic ordering at low temperatures.