The properties of streamers and zonal magnetic structures in magnetic electron drift mode turbulence are investigated. The stability of such large scale structures is investigated in the kinetic and the hydrodynamic regime, for which an instability criterion similar to the Lighthill criterion for modulational instability is found. Furthermore, these large scale flows can undergo further nonlinear evolution after initial linear growth, which can lead to the formation of long-lived coherent structures consisting of self-bound wave packets between the surfaces of two different flow velocities with an expected modification of the anomalous electron transport properties.