This paper presents a model-free fault detection technique based on the use of a specific spectral analysis tool, namely, squared coherency functions. The fault-free dynamic behaviour of the plant considered is described by a stochastic linear state equation, where the stochastic part is due to unpredictable external disturbances. A fault is assumed to be a nonlinear dynamic perturbation of the linear plant dynamics. The detection of the fault is achieved by on-line monitoring the estimates of a squared coherency function that is sensitive to the occurrences of non-linear events affecting the plant dynamics. A theoretical analysis of the fault-detectability issue is made and an original algorithm for a low-bias estimation of the squared coherency function is exploited to minimize the false-alarm rate. Finally, experimental results obtained by using real data concerning the three-tank benchmark problem are reported, showing the effectiveness of the proposed methodology.