Recently Eriksson and Ljunggren (Langmuir 1995, 11, 2325) established theoretically that in some cases the Young contact angle equation corresponds to a maximium of the energy of the system (that is an unstable equilibrium) rather than to a minimum. In fact, these authors have found out an apparent paradox in the classical field of interfacial thermodynamics. Indeed, it is known from the experiment that bubbles or droplets attached to smooth solid surfaces tend to form an equilibrium contact angle, theta, whereas it is shown in ref 1 that under some conditions the fluid particles should avoid formation of an equilibrium contact angle because of an unstable equilibrium. Below we extend the analysis of Eriksson and Ljunggren to demonstrate that the conditions for the stability of particle attachment are different depending on whether the fluid particle contains an independent component, i.e. a component whose chemical potential is independent from those of the components in the surrounding medium. The results show that the equilibrium contact angle corresponds to an unstable equilibrium only when (i) 90 degrees < theta < 180 degrees and (ii) the independent component is missing. In all other cases the equilibrium contact angle corresponds to the stable configuration of the attached fluid particle. These conclusions can be important not only for the specific problem about the bridging cavities as an explanation of the hydrophobic surface force but also for the whole broad field of wetting and spreading.