Space observations in the solar wind and simulations of high Mach number bo
w-shocks have detected particle populations with two coexisting nongyrotrop
ic ion species. We investigate the influence of these two sources of free e
nergy on the stability of parallel (with respect to the ambient magnetic fi
eld) and perpendicular propagation. For parallel modes, we derive their dis
persion equation in a magnetoplasma with protons and alpha particles that m
ay exhibit stationary nongyrotropy (SNG) and discuss the characteristics of
its solutions. Kinetic simulations study the behaviour of perpendicular el
ectrostatic (Bernstein-like) waves in a plasma whose ion populations (posit
rons 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 specie
s does not significantly enhance the parallel SNG instability already found
for media with only one nongyrotropic species, whereas it strongly intensi
fies the growth of Bernstein-like modes in TNG plasmas.