Recent experimental and theoretical findings suggest that the concept of time-dependent instantaneous frequency(IF) is required to comprehensively describe ion motion and mass spectra generation in Fourier transform mass spectrometry (FTMS). Here, we derive a set of differential equations describing ion motion in ion cyclotron resonance (ICR) and Orbitrap FTMS mass analyzers from the IF standpoint. A moving ion is represented by two 2D oscillators: first with oscillations coupled in the radius-azimuth, (r, phi), and second in the radius-z axis, (r, z), coordinate planes. The presented description is thus fundamentally different from a standard representation of ion motion in FT-ICR MS in a form of a superposition of cyclotron and magnetron radii. Analysis of ion motion with the developed theory validates the hypothesis that time-dependent IF is the most probable characteristic condition of ion motion in FTMS mass analyzers. Application of IF theory improves understanding of FTMS fundamentals and should advance FTMS implementation and practice. For instance, the obtained relations between an ion's IF values and mass-to-charge ratios may be used to refine calibration and frequency shift equations. Other envisioned benefits are improved descriptions of ion RF excitation and transient generation processes, as well as of an influence of a space-charge and of an image charge fields. (C) 2014 Elsevier B.V. All rights reserved.