Time-resolved data on intense REB self-focusing in 'MIRAGE' (V=0.8 MV, I=200 kA) and 'KALMAR' (V=0.4 MV, I=150 kA) devices are presented. The 5 ns frame-exposure X-ray photography data corroborate very well with the sharp e-beam focusing reported previously in 'MIRAGE'. The instantaneous current density and power flux in 'MIRAGE' were up to 80 MA cm-2 and up to 6*1013 W cm-2, respectively, exceeding the corresponding time-integrated values by an order of magnitude. The REB sharp focus was seen to wander all over the time-integrated focusing area. The REB behaviour in the 'KALMAR' diode up and downstream from the anode was studied using X-ray pinholes. The FWHM REB focal spot diameter seen in direct time-integrated recording, in 30 ns and 5 ns exposure frames was 2.5-3.5 mm, 1.5-2 mm and 1-1.5 mm, respectively. Data on focal spot-size time dependence were obtained.