Djurhuus plays for the "Akademisk" chess club, which is tied to the University of Oslo.

In 1991 he became the European Junior Champion, ahead of Vladimir Kramnik among others.

His Grandmaster title was gained after scoring a norm at the Chess Olympiad in Manila in 1992, and two norms at Gausdal, in the 1994-1995 tournament, and the 1995-1996 tournament.

With Black, Djurhuus regularly employs the King's Indian against 1.d4, and the Sicilian Defence against 1.e4.

[1] White: Edvīns Ķeņģis Black: Rune Djurhuus Opening: French Defence Event: Gausdal International, 1991 1.e4 e6 2.d4 d5 3.Nd2 Nf6 4.e5 Nfd7 5.f4 c5 6.c3 Nc6 7.Ndf3 Qb6 8.Ne2 cxd4 9.cxd4 Be7 10.a3 0-0 11.Ng3 f6 12.Bd3 fxe5 13.fxe5 (Diagram) 13...Ndxe5 14.dxe5 Nxe5 15.Be2 Bd7 16.Nxe5 Qf2+ 17.Kd2 Rac8 18.Qb3 Bg5+ 19.Kd3 Rf4 20.Nf3 Be8, White resigns.