Heating device for heating in particular noncircular, hollow components, - comprising at least one inner induction coil which penetrates the component to be heated, and comprising at least one element (5, 5') which influences the magnetic field forming during operation of the heating device, which element - is positioned in regions of the component to be heated which heat up more quickly than the other regions, for example because they are thinner, between the inner induction coil and the component to be heated, and thereby weakens the magnetic field in this region, and/or - is positioned in regions of the component to be heated which heat up more slowly than the other regions, for example because they are thicker, within the inner induction coil, and thereby strengthens the magnetic field in this region, whereby comparatively even heating can be achieved, and/or - comprising at least one outer induction coil which surrounds the component to be heated, and comprising at least one element (5, 5') which influences the magnetic field forming during operation of the heating device, which element - is positioned in regions of the component to be heated which heat up more quickly than the other regions, for example because they are thinner, between the outer induction coil and the component to be heated, and thereby weakens the magnetic field in this region, and/or - is positioned in regions of the component to be heated which heat up more slowly than the other regions, for example because they are thicker, outside the outer induction coil, and thereby strengthens the magnetic field in this region, whereby comparatively even heating can be achieved. - comprising at least one inner induction coil which penetrates the component to be heated, and comprising at least one element (5, 5') which influences the magnetic field forming during operation of the heating device, which element - is positioned in regions of the component to be heated which heat up more quickly than the other regions, for example because they are thinner, between the inner induction coil and the component to be heated, and thereby weakens the magnetic field in this region, and/or - is positioned in regions of the component to be heated which heat up more slowly than the other regions, for example because they are thicker, within the inner induction coil, and thereby strengthens the magnetic field in this region, whereby comparatively even heating can be achieved, and/or - is positioned in regions of the component to be heated which heat up more quickly than the other regions, for example because they are thinner, between the inner induction coil and the component to be heated, and thereby weakens the magnetic field in this region, and/or - is positioned in regions of the component to be heated which heat up more slowly than the other regions, for example because they are thicker, within the inner induction coil, and thereby strengthens the magnetic field in this region, whereby comparatively even heating can be achieved, - comprising at least one outer induction coil which surrounds the component to be heated, and comprising at least one element (5, 5') which influences the magnetic field forming during operation of the heating device, which element - is positioned in regions of the component to be heated which heat up more quickly than the other regions, for example because they are thinner, between the outer induction coil and the component to be heated, and thereby weakens the magnetic field in this region, and/or - is positioned in regions of the component to be heated which heat up more slowly than the other regions, for example because they are thicker, outside the outer induction coil, and thereby strengthens the magnetic field in this region, whereby comparatively even heating can be achieved. - is positioned in regions of the component to be heated which heat up more quickly than the other regions, for example because they are thinner, between the outer induction coil and the component to be heated, and thereby weakens the magnetic field in this region, and/or - is positioned in regions of the component to be heated which heat up more slowly than the other regions, for example because they are thicker, outside the outer induction coil, and thereby strengthens the magnetic field in this region, whereby comparatively even heating can be achieved.