Power semiconductor devices in GaN technology include an integrated auxiliary (double) gate terminal and a pulldown network to achieve a normally-off (E-Mode) GaN transistor with threshold voltage higher than 2V, low gate leakage current and enhanced switching performance. The high threshold voltage GaN transistor has a high-voltage active GaN device and a low-voltage auxiliary GaN device wherein the high-voltage GaN device has the gate connected to the source of the integrated auxiliary low-voltage GaN transistor and the drain being the external high-voltage drain terminal and the source being the external source terminal, while the low-voltage auxiliary GaN transistor has the gate (first auxiliary electrode) connected to the drain (second auxiliary electrode) functioning as an external gate terminal. A pull-down network for the switching-off of the high threshold voltage GaN transistor may be formed by additional auxiliary low-voltage GaN transistors and resistive elements connected with the low-voltage auxiliary GaN transistor.