Priority two was a type of communiqué used within the Federation, including Starfleet, that noted messages of less urgent concern than priority one.

In 2369, Captain Edward Jellico ordered Commander William T. Riker to open a secure channel to Admiral Alynna Nechayev, priority two, after the USS Enterprise-D detected only residual traces of theta-band subspace emissions coming from Celtris III. (TNG: "Chain of Command, Part I")