In this paper, the single bunch fast transverse instabilities of the electron beam in the ILSF storage ring due to the RF cavity impedance are investigated. We consider Satoh’s formalism (that studied mode coupling instabilities based on the Vlasov equation) and Lindberg’s formalisms (that studied mode coupling instabilities based on the Fokker–Planck equation). The Lindberg formalisms are rewritten to broad-band RF cavity impedance. It is shown that the zero chromaticity limits of both approaches completely coincide. In addition, we discuss the current threshold at high chromaticity that includes higher-order azimuthal and radial modes.