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The amplitude-independent mechanical quality factors (reciprocal internal frictions) of the binary alloys 98Cu–2Be and 94Cu–6Be, and the commercial alloys Cu–Be “10” (C17 500), phosphor bronze “A” (C51 000), and silicon bronze “A” (C65 500) were measured in the temperature range 50 mK–300 K. This study was motivated by the need to identify materials with very low acoustic losses, which could be used for the fabrication of resonant-mass detectors of gravitational radiation. Data were obtained from measurements of 1 kHz torsional modes of mechanical resonators configured to minimize extraneous internal friction effects. Flexural mode measurements at 9 kHz gave substantially the same quality factor for the 94Cu–6Be as seen at 1 kHz from 50 mK to 10 K. The measured quality factor of this alloy of about 40 million at 50 mK is the largest that has ever been observed in a copper alloy. High resolution resonator frequency data below 10 K are shown to exhibit a temperature dependence which has been associated with dislocation motion in pure elemental metals. © 1999 American Institute of Physics.