Critical heat fluxes have been measured for upward flow of water in annuli for low flow rates and low pressure under sub-cooled and low-quality conditions. Critical heat flux generally occurred under slug flow conditions with large void fractions . At mass velocities greater than ~180 kg/m²s, simple correlations of CHF were obtained. The measured critical heat fluxes were much lower than those predicted by other correlations which nominally should apply to the experimental conditions. At mass velocities less than ~180 kg/m²s, a minimum in CHF was observed as the exit quality was raised through zero. Critical heat flux values under these conditions were significantly less than those predicted for saturated pool boiling at the same pressure.