Abstract Nelson, D. J., Instantaneous Higher Order Phase Derivatives, Digital Signal Processing 12 (2002) 416–428 We present methods, based on the short time Fourier transform, which may be used to analyze the structure of multicomponent FM modulated signals instantaneously in time and frequency. The methods build on previously presented cross-spectral methods. In this paper, we introduce the concept of higher order short time Fourier transform phase derivatives, which may be used to estimate signal trajectories instantaneously in both time and frequency and to determine convergence of the remapped time–frequency surface. The methods are applied to synthesized data and speech signals.