Those two are Mordecai and Rigby's future counterparts who appeared in "Mordecai and the Rigbys". In the future, they were millionaire singers and had all the things they ever wanted (Future Rigby had a shark tattoo on his armpit and Future Mordecai might have finally dated Future Margret). They also pretend to have British accents like the One Direction band and never take their sunglasses off.
They appeared when Mordecai accidentally spilled a can of soda on some record players. Future Mordecai and Future Rigby taught their younger selves how to play the instruments in a good way. On the night of the show, Mordecai and Rigby were doing so well while singing Party Tonight until Mordecai realized they were lip-syncing because the guitar music and the lyrics he and Rigby were signing came only from the CD.
Mordecai and Rigby decided to stop what they were doing which caused their future selves to vanish and broke up their band.
In House Rules, a fat older version of Mordecai with a white beard and hair appeared.