Singlet-triplet pair (STP) Green functions are formulated and studied for the s-d exchange model of dilute magnetic alloys having a single magnetic impurity. Special poles of these STP Green functions (on the unphysical sheet) represent quasibound pair states commonly assumed responsible for the anomalous low-temperature properties of these systems. The STP Green functions are evaluated by an approximate decoupling procedure along with additional approximations for the single-particle averages. For a ferromagnetic interaction, the triplet states show no pole except at zero temperature. A singlet-triplet pole is found for finite temperature for an antiferromagnetic interaction, no pure singlet pole being found except for T=0. These results follow from evaluation of the poles which involves conditions on both the real and the imaginary parts of the frequency; the more common but incorrect evaluation on the real frequency axis leads to quite different conclusions. This singlet-triplet pole corresponds to a low-temperature state possessing a magnetic moment. A range of values of polarization of the conduction electrons (μα) is found to be consistent with the existence of such a quasibound state: 0<μα<=μcrit The maximum μcrit increases with temperature. A comparison is made with certain conclusions of Schrieffer and Wolff, and some differences appear. The results found differ substantially from a parallel calculation made by some of the authors on the Anderson model.