Using the electron drift‐kinetic equation and a hydrodynamic description for the ions new nonlinear vortex equations are derived taking into account the parallel trapping of the electrons in the positive potential regions. It is shown that the usual integration procedure for finding the coherent vortex structures for theE×Bflows in the fluid description can be generalized to include the parallel accelerationeE∥∂f/∂v∥producing the electron holes in the phase space. An example is considered in some detail.