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A party was being held there for the US ambassador's deputy, George Curtis Moore.
Along with Mr Moore, those taken hostage include the Saudi ambassador, Sheikh Abdullah al Malhouk, his wife, the US ambassador to Sudan, Cleo Noel Jr, the Belgian charge d'affaires, Guy Eid, and his Jordanian counterpart, Adli al Nasser.
Reports say eight hooded gunmen entered the building firing guns and then tied up the hostages.
Mr Noel and Mr Moore have been wounded and Sheikh Malhouk, whose four children are in the embassy, says the two men urgently need a doctor - especially Mr Moore who is "even more seriously hurt".
The Japanese envoy has been released unharmed, and his Hungarian counterpart and the Soviet and Yugoslav ambassadors managed to escape without any injuries.
The gunmen have demanded the release of Palestinian militants held by the Israelis, and Sirhan Sirhan - held in a US prison - who assassinated Senator Robert Kennedy.
Also, they want the release of members of West Germany's Bader-Meinhoff gang, who support the Palestinian cause, and 90 Arab militants and military officers held in Jordan.
Unless a 24-hour deadline is met the hostages would be killed, the gunmen have said.
At last year's Munich Olympics, members of Black September seized nine Israeli athletes who were killed along with five hostage takers and a German policeman in a gun battle.
And last December, four members of the group occupied the Israeli embassy in the Thai capital Bangkok.
Six Israelis and two Thai hostages were released unharmed.
No police guards
Sudanese troops and armoured cars have been placed near to the embassy, and the government has been in emergency talks on how best to deal with the crisis.
Unusually, no police guards were on duty around the embassy when the reception for Mr Moore - who is due to leave Khartoum for another post in the US - was taking place.
Reports suggest they were busy dealing with national unity celebrations.
They mark the first anniversary of an agreement ending seven years of civil war between the Central Government of Khartoum and rebels in the south.
The next day, a request by the gunmen for a plane to take them and the hostages to the US was rejected by the American and Sudanese authorities.
Twelve hours later, Cleo Noel Jr, 54, George Curtis Moore, 47, and Guy Eid, 38, were murdered.
The gunmen called the three men enemies of the Palestinian cause, according to Sheikh Malhouk.
In the following two days of the siege, reports said the gunmen had been prepared to kill themselves and the remaining hostages if Sudanese troops entered the embassy in a rescue operation.
At the time, the US State Department suspected the Palestinian Liberation Organisation and Fatah - both led by Yasser Arafat - of involvement in the planning and directing of the siege.
One US official believed Mr Arafat tried to disown the operation by offering to intervene to end the siege.
The Sudanese government refused to compromise with Black September and 60 hours after the siege started the hostages were released and the eight gunmen surrendered.
In June 1974, a court in Sudan sentenced them to life in prison - the US had called for the death penalty - but their sentences were commuted to seven years.
They were then sent to Cairo.
Three of them disappeared and the rest served out their sentences in an Egyptian jail.
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