In order to obtain atomic resolution in a transmission electron microscope, a piezo-driven nanostage with subnanometer stability is under development. Inertial sliding motion is used to move the nanostage table in the plane perpendicular to gravity. One of the most important parameters on the way to such a nanostage is the design of the nanostage table supports. Through several experiments, the stability of two different nanostage table supports is studied : a kinematic and a nonkinematic support. In order to explain the submicrometer and nanometer stage table drift measured in the direction parallel to gravity, a subnanometer contact theory is presented. This theory explains the stage table drift by the following parameters : the size of the apparent contact area of the support, the gravity forces working on the support, the multimolecular layer of adsorbed water molecules on all contact surfaces, creep in the contact points and settling of the contact through microsliding at the contact points. For the initial placement of a nonkinematic support in ambient air with an apparent contact area size of 15x15 mm(2), a stage table drift of 100 nm over 30 min was measured, which almost exactly followed a logarithmic curve. This drift reduced to about 45 nm when the support was placed in a low vacuum, where the number of layers of adsorbed water molecules on the support surfaces is reduced to one or two. Filling the vacuum chamber with nitrogen gas resulted in an even lower stage table drift (25 nm). Stage table drift after single inertial sliding steps is about 25% of the initial amount of drift. In case of a kinematic support, the apparent contact area reduces significantly and stage table drifts after initial placement of 1 up to 3 nm were found. The drift after single inertial sliding steps is on the same order of magnitude. These drifts are attributed to contact creep, which was minimized by optimization of the material selection of both contact surfaces. A combination of two hard surfaces showed almost no creep at the subnanometer level. Therefore, this highly stable kinematic support suits the nanostage application very well.