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We have measured the effective resistance of a Josephson junction and of an rf SQUID cooled at a temperature between 18 mK and 35 mK. From a fit of the data with a simplified solution of the master equation describing the system dynamics we found for both devices an effective resistance R/spl ap/4-5 M/spl Omega/. This value, in the same system cooled at 5 mK, would lead to a decoherence time of approximately 1.1 /spl mu/s allowing one to perform measurements of the Rabi oscillations having a tunneling frequency of the order of few MHz. This value is very promising also for the realization of qu-bits realized by means of Josephson devices.