MgAl2O4 samples were microwave sintered to near-full density in rapid processes with heating rates on the order of 100 degrees C/min and zero isothermal hold. The experiments were carried out using a gyrotron system for microwave processing of materials operating at a frequency of 24 GHz with a maximum power of 6 kW. In the regimes with a preset heating rate sustained by the automatically regulated microwave power, the maximum achieved density was about 95% of the theoretical value in pristine MgAl2O4 samples (maximum sintering temperature 1650 degrees C) and about 97% in 1 wt.% Y2O3-doped samples (1700 degrees C). In the regimes with a fixed microwave power (about 3.5 kW), translucent spinel samples with a relative density above 99% were obtained at 1700 degrees C. The duration of the high-temperature stage of sintering was 1.5-10 minutes. The suggested mechanism responsible for the enhanced densification involves development of a thermal instability and formation of transient liquid phases at grain boundaries. The estimated specific absorbed power in the samples during the high-temperature stage of ultra-rapid microwave sintering was 27-80 W/cm(3), similar to the values observed in dc field-assisted flash sintering experiments.