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The device, believed to contain 300lbs (136kg) of explosive, went off close to the officers' mess at Rheindahlen, 50 miles (80km) from the West German capital Bonn.
Twenty-seven West Germans and four Britons were hurt in the bombing at 2230 local time.
The force of the blast ripped up the road and caused extensive damage to parked cars and surrounding buildings.
The injured have been treated for shock and wounds caused mainly by flying glass. Firefighters at the scene say none of the injured are in a critical condition.
Army spokesman, Nigel Gillies, said: "Indeed we were very lucky that people were not killed."
Mr Gillies said the fact that it was night-time when the bomb went off and the heavy curtains at the base had helped to protect people.
Most of the injured were German officers and their wives, who were enjoying a farewell party at the base.
The injured have been taken to the RAF hospital at Wegberg, a few miles south of Rheindahlen, near the Dutch border.
The bomb caused parts of the ceiling to collapse and doors were ripped from their frames. A police spokesman said the blast blew out windows in buildings several hundred yards away.
A German air force officer at the base said: "We are investigating the possibility that there may be other bombs on the base."
Servicemen have been put on alert and police have sealed off the area around the barracks.
Public roads run through the middle of the base, which is the Army's largest in Europe. Service personnel, families and civilian staff make up the community.
All vehicles are being checked by soldiers to stop any other attempts to breach security after the bombers drove into the open base.
Armed Forces Minister John Stanley said Rheindahlen was on a higher state of security alert than normal at the time of the attack.
Mr Stanley said if this had not been the case, casualties would have been much higher.
A man speaking in English had telephoned a warning to the German press before the blast, Mr Stanley confirmed.
An internal investigation is to be held but Mr Stanley has spoken to MPs about the "immense difficulties" of ensuring total security on such a sprawling base.
A Ministry of Defence spokesman has denied that the public have unrestricted access to the mess area although he said there are "different security levels at various parts of the base".
The IRA later said it had carried out the bombing of the Rheindahlen barracks.
A statement from the IRA said: "Our unit's brief was to inflict a devastating blow but was ordered to be careful to avoid civilian casualties."
The National Democratic Front for the Liberation of West Germany, a previously unheard of group, also claimed to have been behind the attack.
More than 12,000 service personnel were stationed at the base. It was the joint headquarters of the British Army of the Rhine and the Royal Air Force.
The British Army of the Rhine was renamed British Forces Germany (BFG) in 1994.
UK troop numbers in Germany have fallen to around 25,000. The RAF has left but there are 11 Lynx and Gazelle helicopters based at Gutersloh.
IRA attacks in Europe
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