The inside of a time‐stationary strong electrostatic potential structure is characterized by the absence of thermal plasma and by the presence of electron and ion beams, the beam energies being related to the local plasma potential. The operation of collecting and emitting Langmuir probes and double probes within such potential structures is analyzed. It is demonstrated that a floating double probe will not measure the electric field of a strong potential structure without substantial reinterpretation of the potential between the probes. A prescription for the reinterpretation is given. Some probe–surface effects are considered, as are the effects of strong magnetic fields.