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Magnetic interactions have been investigated in Cu(Mn) and Cu(Fe) alloys with concentrations ranging from several hundred to several thousand ppm. In each system two sets of alloys were prepared in different ways to test for sensitivity to structrual modifications. In the Cu(Mn) alloys there was very little difference in magnetic properties of the two sets of alloys which is consistent with the expectation that the Cu(Mn) alloys form good random solid solutions. The magnetic properties were compared with the recent mean-random-field theory of Klein in the low-temperature limit. It was found that the theory is able to explain the concentration dependence of the initial susceptibility and also gives a semiquantitatively correct description of the magnetization to 100 kOe. In the Cu(Fe) alloys the results confirm in part recent work of Tholence and Tournier who, working with much more dilute samples, showed that there exist isolated Fe atoms and ferromagnetically coupled Fe-Fe pairs. The pair magnetization saturates at ∼ 60 kOe for T≲4 °K and each pair has associated with it a spin of ≃ 3. The pair concentration was determined from magnetization and recent Mössbauer experiments in several different sets of alloys. It was shown that this pair density depends sensitively on sample-preparation techniques and cold work, i.e., on modifications of the structure of these supersaturated alloys. It is therefore argued that the pairs are not coupled by long-range Ruderman-Kittel-type interactions but rather they should be regarded as near-neighbor pairs acting as a diatomic molecule dissolved in the copper matrix. The most concentrated alloys in each set of samples (0.6 at.%) exhibited remanence below 3.5 °K. The magnitude of the remanence was proportional to the pair densities in the respective sample sets, suggesting that the ordering was a cooperative effect between the pairs through a mechanism that is not clearly defined. It was shown how the spin-glass transitions recently observed by Svensson in cold-worked alloys could be understood in terms of the breaking up of pairs and other clusters—with a subsequent return to a more random alloy. Finally, the 1.6 °K spin polarization associated with an isolated Fe impurity to ≅100 kOe is compared to two Brillouin functions; one corresponding to T=1.6 °K and the second to T=30.6 °K (≃1.6+TK). The second function fits the data fairly well but there is no theoretical justification for this agreement.