  A detailed study is presented of the counterrotating model (CRM) for
electrovacuum stationary axially symmetric relativistic thin disks of infinite
extension without radial stress, in the case when the eigenvalues of the
energy-momentum tensor of the disk are real quantities, so that there is not
heat flow. We find a general constraint over the counterrotating tangential
velocities needed to cast the surface energy-momentum tensor of the disk as the
superposition of two counterrotating charged dust fluids. We then show that, in
some cases, this constraint can be satisfied if we take the two counterrotating
tangential velocities as equal and opposite or by taking the two
counterrotating streams as circulating along electro-geodesics. However, we
show that, in general, it is not possible to take the two counterrotating
fluids as circulating along electro-geodesics nor take the two counterrotating
tangential velocities as equal and opposite. A simple family of models of
counterrotating charged disks based on the Kerr-Newman solution are considered
where we obtain some disks with a CRM well behaved. We also show that the disks
constructed from the Kerr-Newman solution can be interpreted, for all the
values of parameters, as a matter distribution with currents and purely
azimuthal pressure without heat flow. The models are constructed using the
well-known "displace, cut and reflect" method extended to solutions of vacuum
Einstein-Maxwell equations. We obtain, in all the cases, counterrotating
Kerr-Newman disks that are in agreement with all the energy conditions.
