The growth of single crystals of tetragonal HEW lysozyme and thaumatin I into glass capillaries was monitored by time lapse video-microscopy. The crystals were obtained by unidirectional transport of the precipitating agent through capillaries of internal diameter ranging from 0.2 to 1.2 mm, using the gel acupuncture technique. For crystals growing from true protein solutions, the measured average growth rates varies with capillary diameter from 1.7 to 3.7 ,~/s for thaumatin and from 2.8 to 22 ~,/s for lysozyme. The measured average growth rates for crystals growing into gelled protein solutions were 1.8 ,~/s for thaumatin and 2.5 ,~/s for lysozyme. The trend in the variation of the growth rate with time is similar and suggests that, for capillaries with internal radius lower than 0.8 mm, diffusion dominates the global mass transport control. However, the existence of convection rolls near the crystal-solution interface and close to zones with high density gradient cannot be discarded.