Very-high-speed divide-by-four circuits have been fabricated by using modulation-doped GaAs/GaAlAs high-electron-mobility transistors. The circuits consist of two T-connected D-flip-flops and are capable of operating at 3.6 GHz with a power dissipation of 0.46 mW per gate at room temperature, and at 5.2 GHz with a power dissipation of 0.78 mW per gate at 77 K. The speed-power products achieved are the lowest ever reported.