Analysis of the generalized cross‐field current instability is carried out in which cross‐field drift of both the ions and electrons and their temperatures are permitted to vary in time. The unstable mode under consideration is the electromagnetic generalization of the classical modified‐two‐stream instability. The generalized instability is made of the modified‐two‐stream and ion‐Weibel modes. The relative importance of the features associated with the ion‐Weibel mode and those of the modified‐two‐stream mode is assessed. Specific applications are made to the Earth’s neutral sheet prior to substorm onset and to the Earth’s bow shock. The numerical solution indicates that the ion‐Weibel mode dominates in the Earth’s neutral sheet environment. In contrast, the situation for the bow shock is dominated by the modified‐two‐stream mode. Notable differences are found between the present calculation and previous results on ion‐Weibel mode which restrict the analysis to only parallel propagating waves. However, in the case of Earth’s bow shock for which the ion‐Weibel mode plays no important role, the inclusion of the electromagnetic ion response is found to differ little from the previous results which treats ions responding only to the electrostatic component of the excited waves.