Phase relations in silicon and germanium nitrides (Si3N4 and Ge3N4) were investigated using a Kawai-type multianvil apparatus and a laser-heated diamond anvil cell combined with a synchrotron radiation. The pressure-induced phase transition from the to (cubic spinel-type structure) phase was observed in both compositions. We observed the coexistence of the and phases in Si3N4 at 12.4GPa and 1800 degrees C, while the appearance of single phase -Ge3N4 was observed at pressures above 10GPa. Our observations under higher pressures revealed that -Si3N4 and -Ge3N4 have wide stability fields and no postspinel transition was observed up to 98GPa and 2400 degrees C in both compositions. Using the room-temperature compression curves of these materials, the bulk moduli (K-0) and their pressure derivatives (K-0) were determined: K-0=317 (16)GPa and K-0=6.0 (8) for -Si3N4; K-0=254 (13)GPa and K-0=6.0 (7) for -Ge3N4.