Quadrupole resonance (QR) technology for explosives detection is of crucial importance in an increasing number of applications. For landmine detection, where the detection system cannot be adequately shielded, QR has proven to be highly effective if the QR sensor is not exposed to radio frequency interference (RFI). However, strong non-Gaussian RFI in the field is unavoidable, making RFI mitigation a critical part of the signal processing. In this paper, a statistical model of the non-Gaussian RFI is presented. The QR model is used within the context of an adaptive filtering methodology to mitigate RFI, and this approach is compared to other RFI mitigation techniques. Results obtained using both simulated and measured QR data are presented.