The Spallation Neutron Source accelerator systems will provide a 1 GeV, 1.44 MW proton beam to a liquid mercury target for neutron production. The accelerator complex consists of an H- injector capable of producing 38 mA peak current, a I GeV linear accelerator, an accumulator ring and associated transport lines. The linear accelerator consists of a Drift Tube Linac, a Coupled-Cavity Linac and a Superconducting Linac which provide 1.5 mA average current to the accumulator ring. The staged beam commissioning of the accelerator complex is proceeding as component installation progresses. Recently, the normal-conducting linear accelerator was beam commissioned. A number of beam dynamics and beam quality measurements will be reported, including the measurement of transverse emittances in the H- injector, and the evolution of halo and emittance along the linac.