The aim of this work is to propose a novel approach for the estimation of the Instantaneous Angular Speed (IAS) of rotating machines from vibration measurements. This work is originated from the organisation, by the authors of this paper, of a contest during the conference CMMNO 2014, that was held in Lyon, december 2014. One purpose of the contest was to extract the IAS of a wind turbine from a gearbox accelerometer signal. The analysis of contestant contributions led to the observation that the main source of error in this exercise was the wrong association of one selected and tracked harmonic component with one mechanical periodic phenomenon, this association being assumed as an a priori hypothesis by all the methods used by the contestants. The approach proposed in this work does not need this kind of a priori assumption. A majority (but not necessarily all) periodical mechanical events are considered from a preliminary analysis of the kinematics of the machine (harmonics of shaft rotation speeds, meshing frequencies ...). The IAS is then determined from probability density functions that are constructed from instantaneous spectra of the signal. The efficiency and robustness of the proposed approach are illustrated in the frame of the CMMNO 2014 contest case. Nomenclature Ω: IAS (Instantaneous Angular Speed) (in Hz) ω: argument of the probability density function (pdf) of the IAS (in Hz) A(f): whitened instantaneous spectrum (dimensionless), depending on the frequency f (in Hz) Ω min : minimum value of the a priori IAS uniform law (in Hz) Ω max : maximum value of the a priori IAS uniform law (in Hz) H i (i ∈ [1...n]): orders of the mechanism, with respect to the IAS (dimension-less) [Ω|H i ]: pdf of the IAS knowing H i , function of ω (in Hz) [Ω j |Ω j+k ]: pdf of the IAS at time j knowing the IAS at time j + k, function of ω (in Hz) [Ω j ] j+k : pdf of the IAS at time j obtained from [Ω j+k ], function of ω (in Hz) γ: standard acceleration for IAS (smoothing parameter), in (Hz 2) [Ω j ] s : smoothed pdf of the IAS at time j, function of ω (in Hz)