We apply metal organic chemical vapour deposition (MOCVD) of HfO2 and of ZrO2 from beta-diketonate precursors to grow high-k gate dielectrics for InAlN/AlN/GaN metal oxide semiconductor (MOS)-high electron mobility transistors (HEMTs). High-k oxides of about 12 nm-14 nm are deposited for the MOS-HEMTs incorporating Ni/Au gates, whereas as a reference, Ni-contact-based 'conventional' Schottky-barrier (SB)-HEMTs are processed. The processed dielectrics decrease the gate current leakage of the HEMTs by about four orders of magnitude if compared with the SB-gated HEMTs and show superior device characteristics in terms of I-DS and breakdown.