We have used the Voyager 1 and 2 Ultraviolet Spectrometers to study the far-ultraviolet emissions from different types of shock waves in the Cygnus Loop. In the southeast and northern parts of the supernova remnant (SNR), we have measured the O VI λ1035 surface brightness from the main blast wave. This value is several times below the average and more than one order of magnitude below the peak O VI brightness in the SNR as measured with Voyager. A simple blast wave model appears able to reproduce the observations in the southeast and the northern parts of the Cygnus Loop but can only account for 10%-15% of the total O VI emission from the Cygnus Loop. The brightest O VI and C III λ977 emission is found coincident with optical filamentation and X-ray enhancements in the northeast. We interpret the observations in the northeast in terms of nonradiative and incomplete shocks whose surface area rises in the optical filamentary regions. We conclude that the bulk of the O VI emission from the Cygnus Loop arises from optically bright clouds within which intermediate-velocity (200±50 km s-1) nonradiative and incomplete shocks are widespread.