A magnetorheological brake device has a stationary holder and two brake components. A first brake component is connected to the holder for conjoint rotation and extends in the axial direction. A second brake component includes a hollow sleeve part which can rotate about the first brake component. A gap is formed between the first and second brake components. At least one, two or more rotatable transmission components are arranged in the gap. The gap is filled with a magnetorheological medium. The first brake component has a core which extends in the axial direction and is made of a magnetically conductive material, and an electrical coil which is wound about the core in the axial direction, such that a magnetic field generated by the electrical coil extends across the first brake component.