An electrical machine includes a stator with a stator body supporting an electrical stator and a rotor. The rotor is supported by a bearing having a radial bearing section forming a radial gas bearing and an axial bearing section forming an axial gas bearing, the stator side parts of these bearing sections being a stator side radial bearing part and a stator side axial bearing part that are rigidly connected to one another and together form a stator bearing structure. The stator bearing structure is mounted to the other parts of the stator by either the stator side radial or axial bearing part being rigidly mounted to these other parts, and the other bearing part are connected to these other parts by an elastic support or not at all.