Abstract: A gradient coil system of a magnetic resonance tomography apparatus is fashioned as a hollow cylinder whose hollow interior cross-section is an ellipse with a minor ellipse axis and a major ellipse axis, and contains first and second transverse gradient coils. A first gradient field having a first gradient can be generated with the gradient coil in an imaging volume, and a second gradient field having a second gradient can be generated in said imaging volume with the second gradient coil. The gradient coils are arranged so that the first and the second gradients exhibit an oblique position relative to the major and the minor ellipse axes.