We study the stability of flow in a heated capillary tube with an evaporating meniscus. The behavior of the vapor/liquid system, which undergoes small perturbations, is analyzed by linear approximation, in the frame of a one-dimensional model of capillary flow, with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes, on the flow stability is studied. The velocity, pressure and temperature oscillations in a capillary tube with a constant wall heat flux or a constant wall temperature are determined. A scenario of a possible process at small and moderate Peclet numbers corresponding to the flow in capillaries is considered. The boundaries of stability, subdividing the domains of stable and unstable flows, are outlined, and the values of geometrical and operating parameters corresponding to the transition from stable to unstable flow are estimated. It is shown that the stable capillary flow occurs at relatively small wall heat fluxes, whereas at high ones, the flow is unstable, with continuously growing velocity, pressure and temperature oscillations. (C) 2004 Elsevier Ltd. All rights reserved.