Two different types of MHD instabilities with rapidly chirping frequency were found to arise in the Globus-M2 spherical tokamak in substantially different frequency ranges. The first type arises at frequencies of an order of 1 MHz in ohmic plasmas at relatively low density $\langle {n}_{{\rm{e}}}\rangle \lt 2\times {10}^{19}{\,{\rm{m}}}^{-3}$ in a wide range of toroidal magnetic fields and plasma currents. This type of instability was identified as compressional Alfvén waves, driven by electrons, accelerated during a sawtooth crush. It was found that the mode frequency is sweeping in time, according to the Berk–Breizman hole–clump nonlinear chirping model. The second type of wave arises in a specific single-swing regime of the central solenoid current with a very narrow plasma column, when the plasma tends to decay at extremely low density $\langle {n}_{{\rm{e}}}\rangle \lt 2\times {10}^{18}{\,{\rm{m}}}^{-3}$ and, in fact, is an instability of the runaway electron beam. The exited modes cover the whole observed frequency range and are divided into several (two or three) frequency regions: approximately 0–30 MHz, 60–120 MHz and sometimes 30–60 MHz. Reconnection of the branches was also observed. Single chirps are more rapid than for 1 MHz Alfvén instability and follow an exponential law. This paper, to our knowledge, is the first report of frequency chirping instabilities excited by accelerated electrons at a spherical tokamak.