Evaporation in restricted domains, e.g. in capillaries, is of industrial importance but is poorly understood. Where the evaporating liquid is a binary mixture, preferential evaporation of the more volatile component occurs initially and the evaporation rate is not constant, indeed it appears to occur in stages. Experiments of evaporation from the entrance of a capillary were performed for various binary mixtures of acetone and water and for pure liquids for comparison. Measurements of mass were taken over time for a range of capillary diameters from 0.6 mm to 2 mm. For simplicity, the experiments were performed with the meniscus "stationary" at the entrance of the tube, rather than allowing the meniscus to recede. The data were analysed and showed that, for the binary mixtures, the evaporation process had two distinct stages for the mixtures. The second stage always had a lower slope than the first, indicating a slower evaporation (similar multistage evaporation processes have been observed for sessile drops of binary mixtures). There are many phenomena at work in this process: surface evaporation; diffusion (or natural convective mass transfer) in the air beyond the capillary; diffusion in the binary mixture; circulation in the liquid; thermal effects of evaporative cooling. These are investigated, comparisons made and further studies are proposed.