A method and apparatus for tensioning a staggered anchorage comprised of a plurality of tension members, which are anchored in a bore hole at various depths, thus having different free steel lengths. For each staggered anchorage, each tension member is tensioned up to a predetermined maximal load and is then subsequently adjusted to the working load. To achieve a consistent elongation reserve of the individual tension member and thus to increase the security of a staggered anchorage, the staggered anchorage is adjusted to the working load, all tension members are adjusted to a reduced elongation (.DELTA.I.sub.w) by a uniform elongation difference (.DELTA.I.sub.max-.DELTA.I.sub.w) relative to the respective elongation (.DELTA.I.sub.max) of the predetermined maximal load. An arrangement for performing the method has a single tensioning plane, which is force interconnected with defined locking elements that are arranged on tension members in clamping planes.