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Monitored drift tube chambers (MDT) are the precision tracking detectors in the muon spectrometer of the ATLAS detector at the Large Hadron Collider (LHC). From simulations of the LHC operating conditions, the count rate in the inner barrel chamber of the muon spectrometer is expected to reach 500 Hz/cm2 and can be ten times higher in the luminosity upgrade under discussion (SLHC). A degradation of the performances of drift tube chambers after extended operation in high-rate environment is usually caused by the formation of deposits on the anode wire. To study MDTs aging, three bundles of short tubes equipped like a final MDT chamber were irradiated in different periods with neutrons and photons using the TAPIRO nuclear reactor and the CALLIOPE gamma facility at the ENEA-Casaccia Research Center (Italy). The MDT performances with respect to accumulated dose were studied with cosmic rays and results on drift and tracking properties are presented.