Wireless device technology operating in the millimetre-wave regime (30 to 300 GHz) increasingly needs to offer both high performance and a high level of integration with complementary metal–oxide–semiconductor (CMOS) technology. Aligned carbon nanotubes are proposed as an alternative to III–V technologies in such applications because of their highly linear signal amplification and compatibility with CMOS. Here we report the wafer-scalable fabrication of aligned carbon nanotube field-effect transistors operating at gigahertz frequencies. The devices have gate lengths of 110 nm and are capable, in distinct devices, of an extrinsic cutoff frequency and maximum frequency of oscillation of over 100 GHz, which surpasses the 90 GHz cutoff frequency of radio-frequency CMOS devices with gate lengths of 100 nm and is close to the performance of GaAs technology. Our devices also offer good linearity, with distinct devices capable of a peak output third-order intercept point of 26.5 dB when normalized to the 1 dB compression power, and 10.4 dB when normalized to d.c. power. Radio-frequency transistors made from aligned carbon nanotubes offer high linearity and an extrinsic cutoff frequency of over 100 GHz.