The evolution of the electromagnetic ions beam instability driven by the reflected ion component backstreaming away from the earth's how shock into the foreshock region is studied by means computer simulation. The linear the quasi-linear states of the instability are found to be in good agreement with known results for the resonant model propagating parallel to the beam along the magnetic field and with theory developed in this paper for the nonresonant mode, which propagates antiparallel to the beam direction. The quasi-linear stage, which produces large amplitude 8B~B, sinusoidal transverse waves and ''intermediate'' ion distribution, is terminated by a nonlinear phase in which strongly nonlinear, compressive waves and ''diffuse'' ion distributions are produced. Additional processes by which the diffuse ions are accelerated to observed high energies are not addressed. The results are discussed in terms of the ion distributions and hydromagnetic waves observed in the foreshock of the earth's bow shock and of interplanetary shocks.