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A mechanism for the antiferromagnetic ordering of a dilute paramagnetic solute in a metal is proposed and discussed in relation to the phenomena that occur in copper-manganese alloys. Long-range antiferromagnetic order results from a static spin-density wave in the electron gas of the metal. This new state of the gas is dynamically self-sustaining as a result of the exchange potentials arising from the spin-density distribution. The paramagnetic solute atoms are then oriented by their exchange interaction with the spin-density wave. The resulting interaction energy more than compensates the increase in energy associated with the formation of the spin-density wave. The theory predicts correctly the magnitude and concentration-dependence of the critical temperature, the anomalous low-temperature specific heat and the anomalous electrical and magnetic properties of the alloys.