We introduce an approach for damage detection in gearboxes based on the analysis of sensor data with the multi-resolution dynamic mode decomposition (mrDMD). The application focus is the condition monitoring of wind turbine gearboxes under varying load conditions, in particular irregular and stochastic wind fluctuations. We analyze data stemming from a simulated vibration response of a simple nonlinear gearbox model in a healthy and damaged scenario and under different wind conditions. With mrDMD applied on time-delay snapshots of the sensor data, we can extract components in these vibration signals that highlight features related to damage and enable its identification. A comparison with Fourier analysis, Time Synchronous Averaging and Empirical Mode Decomposition shows the advantages of the proposed mrDMD-based data analysis approach for damage detection.