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The authors report on the first results of an investigation on the eigenfrequencies and quality factors of vibration of Al 5056 spherical resonators at very low temperatures. In particular the characteristics of the lowest order spheroidal quadrupole mode, relevant for gravitational wave research were measured. The resonators were suspended at the nodal point. Quality factors up to 1.2 10(sup 8) were measured in a bulk sample down to 44 mK. Another spherical resonator was obtained by means of explosively-bonded stacks and showed a maximum quality factor of 2 10(sup 7). The observed quadrupole modes appear to be split into frequency multiplets, because of the broken spherical symmetry, as theoretically predicted. The independence of the modes was measured within one part in 10(sup 5) in amplitude.