Because of the growing interest in real-time stability monitoring, there is a need for online methods that can detect off-nominal behavior in control systems. Therefore, we present a real-time frequency domain method for detecting oscillations in control systems. The method uses recursive Fourier transform for representing the measured time domain signal in frequency domain. Oscillations are then detected by monitoring the norm of the Fourier coefficients over a time window of pre-specified size across a range of frequencies that represent off-nominal behavior for the plant. This method is computationally efficient and requires limited memory, hence it can be used for onboard health monitoring of Unmanned Aerial Systems (UAS). Consequently, we demonstrate the feasibility of using this method for real-time detection of oscillation on the Georgia Tech GT Twinstar (UAS).