The formation of a nanosecond discharge with the use of a Hamamatsu streak-camera and with simultaneously wideband (10 GHz) measurement of voltage and displacement current caused by a streamer in one pulse has been studied. Nanosecond voltage pulses of various amplitudes (16, 20, and 27 kV) were applied across a point-to-plane gap (8.5 mm) filled with air at various pressures (13, 25, 50, 100, and 200 kPa). It was found that the voltage across the gap drops as soon as a streamer appears in the vicinity of the pointed electrode. At the same time, a pre-breakdown current begins to flow. The magnitude of the pre-breakdown current, as well as the voltage drop, is determined by the rate of formation of dense plasma and, accordingly, by the rate of redistribution of the electric field in the gap. The streamer velocity determines the rise time and amplitude of the current. The higher the streamer velocity, the shorter the rise time and the higher the amplitude of the pre-breakdown current. The propagation of a backward and third ionization waves was observed both with the streak camera and by measuring the displacement current. As they propagate, the discharge current increases to its amplitude value.