Abstract: Methods and systems for acquiring offset data for aligning co-rotatable in-line machine shafts. Two sets of offset data, each set for example representing relative displacement in a radial direction between a reference point referenced to one of the shafts and a particular point on the other of the shafts at given angular positions, are collected at a plurality of measurement angular positions. The measurement angular positions are not necessarily the 0.degree., 90.degree., 180.degree. and 270.degree. angular positions at which measurements are traditionally taken. Preferably, measured offset data is collected during continuous rotation of the shafts in their normal direction of rotation or at convenient positions where the rotation is halted. Measured offset data may be collected at as few as three angular positions, but preferably is collected at more than three angular positions, and typically at a multiplicity of angular positions such as thirty or forty.