This article presents the effectiveness of bispectrum analysis for the detection of the rotor unbalance of an induction motor supplied by the mains and a frequency converter. Two diagnostic signals were analyzed, as well as the stator current and mechanical vibrations of the tested motors. The experimental tests were realized for two low-power induction motors, with one and two pole pairs, respectively. The unbalance was modeled using a test mass mounted on a specially prepared disc and directly on the rotor and the influence of this unbalance location was tested and discussed. The results of the bispectrum analysis are compared with results of Fourier transform and the effectiveness of unbalance detection are discussed and compared. The influence of the registration time of the analyzed signal on the quality of fault symptom analyses using both transforms was also tested. It is shown that the bispectrum analysis provides an increased number of fault symptoms in comparison with the classical spectral analysis as well as it is not sensitive to a shorter registration time of the diagnostic signals.