With the ever increase of the complexity and the importance of industrial systems, diagnosis techniques allowing to detect, locate and identify any abnormalities in the system as early as possible, have attracted a lot of attention over the past years. In this paper, we present a diagnosis method for nonlinear dynamical systems, called sparse recovery diagnosis (SRD), based on a dynamical algorithm that estimates a sparse fault vector from few system measurements. The term sparse means that many faults can be considered but only few of them can occur simultaneously. In order to illustrate the performances of this diagnosis method, we apply it to a gear power transmission. This dynamical system is among the most important mechanical components in industrial systems. The gear power transmission model considered in this paper is composed by a two-stage gear for which we take into account the torsional eect of the gears. Dierent sensor and mechanical faults perturbing its operating mode will be modeled and detected by the SRD method.