We report on linearity and robustness of AlN/GaN HEMTs with ultra-thin 4nm AlN barrier for millimeter wave range applications. Static and dynamic I-V characteristics feature high peak transconductance (gmpeak) of 385 mS/mm, and the transconductance exhibits small changes with gate bias. Semi on-state step stress and 24 h stress tests have been carried out on representative AlN/GaN HEMTs on SiC substrate. No catastrophic failure was identified after semi on-state step stress at VGS =-1.5 V up to VDS = 100 V, whereas a gmpeak drop of 26 % was observed in these conditions. Moreover, 24 h stress carried out at different bias voltage along a load line show good robustness of these devices up to VDS = 25 V. In addition, an abrupt gate leakage current increase was identified to be field dependent, and associated with hot spots identified by electroluminescence measurements. Even in presence of a simple SiN passivation without air bridges or field plates, these devices exhibit high power added efficiency up to 40 GHz, thus demonstrating the great potential of AlN/GaN heterostructures.