It is intended to continue at the Tevatron the investigation of deep inelastic muon scattering using an upgraded version of the NA4 spectrometer now in operation at the CERN-SPS.The accurate determination of the nucleon structure functions over a large Q 2 range, up to 400 GeV 2 on H 2 and D 2 are made possible by the distributed target structure of the NA4 spectrometer. In addition the use of heavier targets and the increased muon energy available at the Tevatron will permit to study the effects of the weak interactions of muons through the y-z 0 interference and thus to measure the muon neutral current couplings.