Experimental studies of low-Reynolds number, pressure-driven core–annular flow in a straight capillary tube are reported. The annular film is thin compared with the radius of the tube, and the viscosity of the film fluid is much larger than the viscosity of the core fluid. Photographs show that the film is unstable under all conditions investigated in the experiment. The film fluid collects in axisymmetric lobes that are spaced periodically along the capillary wall. The spacing of the lobes and their translational velocity correspond closely with the wavelength of the most unstable disturbance and phase velocity calculated from linear stability theory. Eventually, the continued growth of the lobes results in the formation of a fluid lens that breaks the inner core.