We report on robust and low-power-consumption InP- and GaN-HEMT Low-Noise-Amplifiers (LNAs) operating in Q-band frequency range. A multi-stage common-gate (CG) amplifier with current reuse topology was used. To improve the survivability of the CG amplifier, we introduced a feedback resistor at the gate bias feed. The design technique was adapted to InP- and GaN-HEMT LNAs. The 75nm gate length InP HEMT LNA exhibited a gain of 18dB and a noise figure (NF) of 3dB from 33 to 50GHz. The DC power consumption was 16mW. The Robustness of the InP HEMT LNA was tested by injecting a millimeter-wave input power of 13dBm for 10 minutes. No degradation in a small signal gain was observed. The fabricated 0.12µm gate length GaN HEMT LNA exhibited a gain of 15dB and an NF of 3.2dB from 35 to 42GHz. The DC power consumption was 280mW. The LNA survived until an input power of 28dBm.