The phase behaviour of a fluid in mesopores just below the critical temperature (T(c)) has been studied experimentally and by molecular dynamics simulations. Experimental results were obtained for the adsorption of sulfur hexafluoride (SF6) on Controlled-Pore Glass (CPG-10) for reduced temperatures T(r) = T/T(c) of 0.857, 0.920 and 0.985. Pore condensation occurs at the two lowest temperatures, whereas at the highest temperature (T(r) = 0.985) a phase transition cannot be detected, indicating that the fluid inside the pore is in a supercritical state. It follows that the pore critical temperature (T(cp)) is lower than the bulk critical temperature. An analysis of unstable and metastable limits for the underlying system is given. Molecular dynamics computer simulations have been performed for a system of Lennard-Jones molecules, where the parameters values chosen simulated the SF6-CPG system. Phase transitions are only present for the lowest temperatures, but the isotherm at T(r) = 0.985 increases monotonically in agreement with experiment. If the fluid-fluid interaction epsilon-FF is decreased, pore condensation occurs at higher relative fugacities f/f(sat). Pore condensation occurs closer to the saturation pressure as the radius R is increased, in agreement with the experimental findings.