This paper introduces the application of third order cyclic statistics for vibration signals in rotating machinery. It is shown for the first time that these vibration signals display third-order cyclostationarity under some conditions. A model of signals modulated in amplitude and phase is used in order to compute the cyclic bispectrum, a third-order cyclic statistical parameter, in the frequency domain. The interpretation and the estimation techniques of this cyclic bispectrum give better understanding of the application of cyclic statistics to mechanical systems. The ambiguity concerning the use of moments or cumulants for the estimates is discussed. Moreover, the difference between them is illustrated with industrial gear signals. Application to the diagnosis of spalling in gear teeth of a U.S. Navy helicopter gearbox demonstrates the effectiveness of this new parameter for a good diagnosis.