The stability of equilibrium configurations of a capillary liquid in a circular cylindrical container with planar ends is investigated. The liquid is under zero gravity conditions, and its wetting angle is constant over the entire solid surface. Attention is focused on the case for which the free surface consists of two disconnected pieces (connectivity components) that bound the connected liquid domain. First we outline the method used to determine critical states with disconnected free surfaces when each connectivity component is axisymmetric. Then we examine the stability of disconnected surfaces for the simple cases that arise when each connectivity component represents a closed sphere or a part of a sphere. Ten configurations were considered that represent all possible combinations of the following connectivity components: A closed sphere (that bounds a gas bubble), a spherical cap in contact with the lateral wall of a cylinder; a spherical cap in contact with a cylinder endwall, and a portion of a sphere (that does not cross the cylinder's axis of symmetry) bounded by a cylindrical wall and a flat endwall. (C) 2000 American Institute of Physics.