A new generic approach to fatigue crack monitoring in aero-engine blades is presented. The approach consists of simultaneously using two new diagnostic features: the real and imaginary parts of the Fourier transform of vibroacoustical signals. This approach is more fundamental than traditional approaches based on the power spectral density, phase spectrum and Hartley transform; each of these approaches is a special case of the proposed approach. Numerical examples are given based on the processing of signals generated using a nonlinear model of tested blades. The generated signals are the forced vibroacoustical oscillations of cracked and un-cracked blades. The numerical examples show that crack detection is more effective when using the new approach than when using the power spectral density approach. The presented experimental results using un-cracked and cracked turbine blades from an aero-engine are matched with numerical results. The proposed approach offers an effectiveness improvement over the traditional approach based on power spectral density.