The influence of fast neutrons on the occupancy and the single tube resolution of ATLAS muon drift detectors was investigated by exposing a chamber built out of 3 layers of 3 short standard drift tubes to neutron flux-densities of up to 16 kHz/cm2 at a neutron energy of E=11 MeV. Pulse shape capable NE213 scintillaton detectors and a calibrated BF3 neutron detector provided monitoring of the neutron flux-density and energy. The sensitivity of the drift chamber to the neutrons was measured to be 4*10-4 by comparing data sets with and without neutron background. For the investigation of tracks of cosmic muons two silicon-strip detectors above and underneath the chamber allow to compare measured drift-radii with reference tracks. Alternatively, the single tube resolution was determined using the triple-sum method. The comparison between data with and without neutron irradiation shows only a marginal effect on the resolution and little influence on the muon track reconstruction.