Capillary instability of long annular viscous liquid layers coating the surface of a cylindrical wire is studied. Effects of Reynolds number, Re, initial disturbance wave numbers, k, and wire radii, s on the growth rate of the instability are considered. The initial disturbance amplitude is chosen as 5% of the initial unperturbed liquid thickness. It is found that the growth rate of the disturbance amplitude is composed of a linear portion, which is well predicted by the linear theory, and a relatively flat portion, which is not predicted by the linear theory and is strongly dependent on the Re, k, and s. A unique feature of this instability is a double pinch-off process (in certain parameter range) which results in the formation of secondary satellite drops.