The detailed analysis of stability of azimuthal oscillations in partially magnetized plasmas with crossed electric and magnetic fields is presented. The instabilities are driven by the transverse electron current which, in general, is due to a combination of E×B and electron diamagnetic drifts. Marginal stability boundary is determined for a wide range of the equilibrium plasma parameters. It is shown that in some regimes near the instability threshold, only the low-frequency long-wavelength oscillations are unstable, while the short-wavelength high-frequency modes are stabilized by the finite Larmor radius effects. Without such stabilization, the high-frequency modes have much larger growth rates and dominate. A new regime of the instability driven exclusively by the magnetic field gradient is identified. Such instability takes place in the region of the weak electric field and for relatively large gradients of plasma density (ρs/ln>1, where ρs is the ion-sound Larmor radius and ln is the scale length of plasma density inhomogeneity). © 2018 Author(s).