The transition between non-resonant (Weibel-type) and resonant (whistler) instabilities is investigated numerically in plasma configurations with an ambient magnetic field of increasing amplitudes. The Vlasov–Maxwell system is solved in a configuration where the fields have three components but depend only on one coordinate and on time. The nonlinear evolution of these instabilities is shown to lead to the excitation of electromagnetic and electrostatic modes at the first few harmonics of the plasma frequency and, in the case of a large ambient magnetic field, to a long wavelength, spatial modulation of the amplitude of the magnetic field generated by the whistler instability.