|Competitor for Bahamas|
|Silver||2008 Beijing||4x400 m relay|
|Gold||2001 Edmonton||400 m|
|Gold||2001 Edmonton||4x400 m relay|
|Silver||2005 Helsinki||4x400 m relay|
|Silver||2007 Osaka||4x400 m relay|
|Bronze||2003 Paris||4x400 m relay|
|Pan American Games|
|Gold||2007 Rio de Janeiro||4x400 m relay|
Moncur's most successful year came in 2001 when he won the gold medal in the 400m and the 4x400m relay at the 2001 World Championships. Moncur has only managed to make one more appearance in the individual final of a major championship, at the 2007 World Championships where he finished 8th.
More success, however, has come has part of the Bahamas relay team. At the 2005 World Championships he (together with Nathaniel McKinney, Andrae Williams and Chris Brown) won a silver medal in 4 x 400 metres relay.
Moncur's personal best time and national record in the 400m is 44.45 seconds, achieved in July 2001 in Madrid. However, Chris Brown tied Moncur's national record at the 2007 World Championships.