A nonlinear two-dimensional computational model has been developed to examine the nonlinear state of the two-stream plasma instability in the equatorial electrojet. The model employed the two-fluid equations for electrons and ions in the vicinity of a constant northward magnetic field perpendicular to an applied electric field. Collisions with neutral species were included along with a viscous representation of the Landau damping of short wavelength modes. The unperturbed plasma was assumed to be homogeneous and isothermal. The simulation confirmed radar observations of isolated Type 1 irregularities (Crochet et al., 1979): (1) horizontally directed waves were dominant and propagated at the acoustic speed, and (2) obliquely directed waves had spectral heights several orders of magnitude lower and propagated at speeds lower than the acoustic speed. The instability appeared to saturate by a rotation of the electric field vector until the component perpendicular to the current density field vector was reduced to a value lower than the critical value for marginal stability. In one dimension this would appear as a 'velocity reduction' mechanism reducing the instability to a marginally stable state.