Air breakdown on runaway electrons was investigated experimentally when the macroscopic electric field approximates to the critical value ( E c ) for runaway of free electrons not only at the cathode but throughout the discharge gap. Since spatial and temporal increment of an avalanche of runaway electrons is sharply reduced at high values of the specific electric field ( E/p ). There is reason to assume that the limiting case of breakdown on runaway electrons with a threshold energy approaching to thermal is realized. Avalanche current of runaway electrons behind the grid anode increased less than a hundred picoseconds and was close to the short circuit current of the gap.