The three-dimensional structure of proteasomes from the archaebacterium Thermoplasma acidophilum has been determined to a resolution of approximately 2 nm from electron micrographs of negatively stained preparations using the method of 'random conical tilting'. The particles turn out to be essentially cylinder-shaped barrels, 15 nm long and 11 nm wide, enclosing a tripartite inner compartiment. An account is given of some of the present limitations which prevent to attain a higher resolution and possible ways to overcome these limitations are indicated.