We present the Herschel SPIRE Fourier Transform Spectroscopy (FTS) atlas for a complete flux-limited sample of local ultraluminous infrared galaxies (ULIRGs) as part of the HERschel Ultra Luminous InfraRed Galaxy Survey (HERUS). The data reduction is described in detail and was optimized for faint FTS sources ,with particular care being taken for the subtraction of the background, which dominates the continuum shape of the spectra. To improve the final spectra, special treatment in the data reduction has been given to any observation suffering from artifacts in the data caused by anomalous instrumental effects. Complete spectra are shown covering 200-671 μm, with photometry in the SPIRE bands at 250, 350, and 500 μm. The spectra include near complete CO ladders for over half of our sample, as well as fine structure lines from [C I] 370 μm, [C I] 609 μm, and [N II] 205 μm. We also detect H 2 O lines in several objects. We construct CO spectral line energy distributions (SLEDs) for the sample, and compare their slopes with the far-infrared (FIR) colors and luminosities. We show that the CO SLEDs of ULIRGs can be broadly grouped into three classes based on their excitation. We find that the mid-J (5<J<8) lines are better correlated with the total FIR luminosity, suggesting that the warm gas component is closely linked to recent star formation. The higher J transitions do not linearly correlate with the FIR luminosity, consistent with them originating in hotter, denser gas that is unconnected to the current star formation. We conclude that in most cases more than one temperature component is required to model the CO SLEDs.