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A new method using the analytic wavelet transform of the stator current signal is proposed for detecting dynamic eccentricity in brushless direct current (BLDC) motors operating under rapidly varying speed conditions. As wavelets are inherently suited for non-stationary signal analysis, this method does not require the use of any windows nor is it dependent on any assumption of local stationarity. The time-frequency resolution obtained is therefore better than other existing techniques such as the short time Fourier transform (STFT). Experimental results are provided to show that the proposed method works over a wide speed range of motor operation and provides an effective and robust way of detecting rotor faults such as dynamic eccentricity in BLDC motors.