Linear Energy Transfer (LET) effects in radiation chemistry are ascribed to the high density of active species in the track structure, resulting in overlapping of spurs. We studied the possibility of spur overlapping in electron beam irradiation at extremely high dose rate, both theoretically and experimentally. Considering differences in overlap mode leads to the concept of a "threshold dose rate", above which spur overlapping may occur, and an "overlapping dose", which is necessary to cause overlapping of spurs even at higher dose rate than the threshold, depending on lifetime and effective volume of reactive intermediates. Using Sandia's pulsed power e-beam system, we irradiated cellulose triacetate (CTA), polymethylmethacrylate (PMMA), polycarbonate (PC) and high density polyethylene (HDPE) at a dose.rate as high as 4 x 10 ~° Gy/s at room temperature in the absence of oxygen. Comparison of the e-beam results with data obtained from gamma irradiation at 0.5 Gy/s showed no dose rate effects based on discoloration sensitivity for CTA, or on scission probabilities of PMMA and PC. For HDPE, the results indicated a slightly lower rate of gel formation under e-beam irradiation, implying that the crosslinking efficiency may be somewhat reduced at the high dose rate.