In a method and apparatus for determining the rotary angular position of a rotary member when measuring unbalance on the rotary member, during an unbalance measuring run the rotary member is twice sensed in the peripheral direction in a given succession in respect of time, resulting in the formation of first and second angle signals which are displaced in respect of time. The two signals are stored, having regard to their spacing in respect of time. The two signals are evaluated for rotating the rotary member, in dependence on the measured angular position of an unbalance, into a balancing position for carrying out a balancing operation on the rotary member.