The RAF, also known as the Baader-Meinhof Gang, mounted a bloody campaign of shootings, bomb attacks and kidnappings against what it saw as the oppressive capitalist state of West Germany from 1977 to 1982. The group officially disbanded in 1998.
Three of the RAF's early members - Andreas Baader, Gudrun Ensslin and Jan-Carl Raspe - died in a high-security prison in Stuttgart on the night of October 18,1977. Authorities ruled the deaths suicides, but Ensslin's brother Gottfried and an author have challenged this.
However prosecutors in the southwestern state of Baden-Württemberg, where the prison is located, said in a statement that "investigations will not resume into the RAF case" because "no new evidence was submitted that would raise questions about the original findings."
The prosecutors dismissed as fake a document suggesting a guard had been pulled off duty from the wing where the prisoners had been staying on the night.
The RAF, born out of the extreme militant fringe of the 1960s student and anti Vietnam war protests, targeted the German political and business elite and US military bases.
Their reign of terror claimed 34 victims, and more were injured in bank robberies and bomb attacks.
After "first-generation" members including Baader and former journalist Ulrike Meinhof were captured, they were jailed in the high security prison Stuttgart-Stammheim and sentenced to mostly life terms.
Meinhof was found hanged in her cell from a rope made of torn bedsheets in May 1976 in what was ruled a suicide.
Baader, Ensslin and Raspe killed themselves late on October 18 the following year, officials said. Raspe and Baader had shot themselves with weapons smuggled in by a lawyer, and Ensslin had hanged herself with a cable.
Another RAF prisoner, Irmgard Möller, tried to stab herself in the heart but survived.