The conflict in South Kordofan began just before South Sudan's independence
Rebels in Sudan say they have shot down a government military aircraft after it had bombed rebel targets.
The Sudan People's Liberation Movement-North (SPLM-North) says the Antonov bomber crashed on Wednesday in the Jau area, South Kordofan state.
The Sudanese authorities have not commented on the rebel claim.
Tens of thousands of people have fled their homes to escape fighting between government troops and rebels in Sudan's South Kordofan and Blue Nile states.
The government plane was shot down on Wednesday afternoon, Arnu Ngutulu Lodi, a spokesman for the SPLM-North, told the AFP news agency.
He said the rebels "shot at it until they saw the wing burning", adding that the aircraft went down near Jau - on the disputed border between Sudan and South Sudan.
The rebel claim has not been independently verified because of restricted access to the area.
Correspondents say the SPLM-North sees itself as continuing in the footsteps of the movement from which it sprang, the SPLM, which now runs South Sudan.
Fighting is said to be vicious, with refugees describing frequent air raids by government forces. The Sudanese military denies claims it is targeting the Nuba ethnic community who are seen as rebel supporters.
The SPLM-North has twice shelled the South Kordofan capital, Kadugli, this month.
The government in Khartoum accuses South Sudan of backing the rebels - a claim denied by Juba.
Last month, US Assistant Secretary of State for the Bureau of Population, Refugees and Migration, Anne Richard, accused the rebels of recruiting child soldiers from the Yida refugee camp in South Sudan.
"We've asked that they not take children to serve as soldiers on the other side of the border," she said, after a visit to Yida.
The camp has been bombed several times by Sudanese forces.
Since South Sudan's independence, tension between the new neighbours has been strained, with rebellions breaking out on either side of the border and a dispute over oil which escalated to the brink of war in April.
However, in September the leaders of both nations signed a deal, mediated by the African Union, to resume oil sales and set up a demilitarised buffer zone.