This paper reports current-voltage characteristics and pressure-voltage transition curves from the weak-current ␣-mode to the strong-current ␥-mode for rf capacitive discharges in N 2 O at frequencies of 2 MHz, 13.56 MHz, and 27.12 MHz. At 2 MHz the rf discharge is mostly resistive whereas at 13.56 MHz and 27.12 MHz it is mostly capacitive. The weak-current ␣-mode was found to exist only above a certain minimum gas pressure for all frequencies studied. N. Yatsenko ͓Sov. Phys. Tech. Phys. 26, 678 ͑1981͔͒ previously proposed that the ␣ − ␥ transition corresponds to breakdown of the sheaths. However, we show that this is the case only for sufficiently high gas pressures. At lower pressure there is a smooth transition from the weak-current ␣-mode to a strong-current ␥-mode, in which the sheaths produce fast electrons but the sheath has not undergone breakdown.