The recently introduced Class-EF power amplifier (PA) has a peak switch voltage lower than that of Class-E PA. However, the value of the transistor output capacitance at high frequencies is typically larger than the required Class-EF optimum shunt capacitance. Consequently, soft-switching operation that minimizes power dissipation during OFF-to-ON transition cannot be achieved at high frequencies. Two new Class-EF PA variants with transmission-line load networks, namely, third-harmonic-peaking (THP) and fifth-harmonicpeaking (FHP) Class-EF PAs are proposed in this paper. These permit operation at higher frequencies at no expense to other PA figures of merit. Analytical expressions are derived in order to obtain circuit component values which satisfy the required Class-EF impedances at fundamental frequency, all even harmonics, and the first few odd harmonics as well as simultaneously providing impedance matching to a 50 Ω load. Furthermore, a novel open-circuit and shorted stub arrangement which has substantial practical benefits is proposed to replace the normal quarter-wave line connected at the transistor's drain. Using GaN HEMTs, two PA prototypes were built. Measured peak drain efficiency of 91% and output power of 39.5 dBm were obtained at 2.22 GHz for the THP Class-EF PA. The FHP Class-EF PA delivered output power of 41.9 dBm with 85% drain efficiency at 1.52 GHz.