Abstract: Apparatus for preventing changes of the position of a machine, such as a measuring machine, has several pneumatic bearings which floatingly support the machine and receive signals from a digital computer to ensure timely selection of resistance which must be offered by the bearings to changes of the position of the machine relative to its support while a mobile part of the machine moves relative to the part which is supported by the bearings. Signals which are stored in the memory of the computer are calculated in advance or are obtained as a result of one or more test runs by taking into consideration all parameters which are likely to impart to the bearing-supported part or parts a tendency to change its or their positions. Such parameters include the distance to be covered by the mobile part, the configuration of the path of movement of the mobile part, the velocity of the mobile part, the mass of the mobile part and of the bearing-supported part or parts, the inertia of the bearings and others.