A procedure has been developed to measure the attenuation of second sound in liquid helium at temperatures nearT&lgr;. The decay rate of a second‐sound resonance in a high‐Qcavity is determined, and data for more than one harmonic is obtained allowing the separation of the attenuation due to bulk fluid from losses at the cavity walls. This method has proven particularly successful nearT&lgr;, where the second‐sound velocity is strongly dependent on temperature and a high degree of temperature stability is needed. Results are given for the temperature range 40 &mgr;K<T&lgr;‐T<40 mK at saturated vapor pressure. With minor modifications the apparatus can be used for measurements at elevated pressure and over a much wider range of temperatures.