Misalignment of multi-bearing rotor systems is one of the most common fault conditions yet it is still not fully understood. There are numerous (and sometimes confusing) accounts in the literature asserting the presence of harmonics in the vibration signal, but no quantitative descriptions are offered. Harmonics may arise, of course, from the nonlinearities in fluid film journal bearings or from the kinematics of flexible couplings, but in this paper only rigidly coupled rotors mounted on idealised linear bearings. It is shown that even for this case, excitation at twice synchronous speed is developed and an expression for the magnitude and phase of the response is derived. Several examples are then studied to give some insight into the magnitude of these harmonic terms which can arise. It is argued that it is precisely because the harmonic terms can arise from diverse sources, a full description of the phenomena has proved somewhat elusive. A brief discussion of the type of rig required to validate the model is given. There is a need to separate the phenomena discussed here from the nonlinearities found in real machines. Some features of the new facility are described.