Space observations in the solar wind and simulations of high Mach number bow-shocks have detected particle populations with two coexisting nongyrotropic ion species. We investigate the influence of these two sources of free energy on the stability of parallel (with respect to the ambient magnetic field) and perpendicular propagation. For parallel modes, we derive their dispersion equation in a magnetoplasma with protons and alpha particles that may exhibit stationary nongyrotropy (SNG) and discuss the characteristics of its solutions. Kinetic simulations study the behaviour of perpendicular electrostatic (Bernstein-like) waves in a plasma whose ion populations (positrons and fictitious singly-charged particles with twice the electron mass, for the sake of simulation feasability) can be time-varying nongyrotropic (TNG). The results show that the coexistence of two gyrophase bunched species does not significantly enhance the parallel SNG instability already found for media with only one nongyrotropic species, whereas it strongly intensifies the growth of Bernstein-like modes in TNG plasmas.</p> <p style="line-height: 20px;"><b>Key words.</b> Magnetospheric physics (plasma waves and instabilities) · Space plasma physics (numerical simulation studies; waves and instabilities)