The viscosities eta of carbon dioxide and xenon have been measured near their critical points and the critical exponent y characterizing the asymptotic divergence, eta ~ |T- Tc|^-y, has been determined. Both fluids yielded exponents in the rangey = 0.041 ± 0.001 and thus also fell in the range y = 0.042 ± 0.002 from our earlier study of four binary liquids. This agreement between experiments is the first evidence that pure fluids and binary liquids are in the same dynamic universality class. A recent theoretical value for y is 0.032. The 30% discrepancy is much greater than the combined errors from experiment and theory. The torsion oscillator viscometer operated at low frequency and low shear rate to avoid systematic errors caused by critical slowing down. Far from Tc the analysis accounted for the crossover from critical to noncritical temperature dependence, where the latter was obtained from previously published correlations. Corrections for gravitational stratification were included close to Tc.