Law enforcement officials in the German state of Lower Saxony released pictures, taken this year, they believe are of Ernst-Volker Staub, 61, and Burkhard Garweg, 47, who are being sought on suspicion of attempted murder and attempted robbery.
Police are also seeking a third member of the group, Daniela Klette, 57, although their most recent photo of her dates back to 1988.
The wanted trio are former members of the Red Army Faction, a radical-left terrorist organization better known as the Baader Meinhof Group, which once terrorized German society with a campaign of bombings, assassinations and kidnappings.
The anti-capitalist group officially disbanded in 1998, but former members have remained on the run, avoiding prosecution for their crimes.
Two attempted armed robberies
Suspected of involvement in a string of violent crimes, the three are most recently under investigation in two failed attempts to rob armed security vans last year.
The public prosecutor's office in the town of Verden said that in the first attempted robbery, in the town of Stuhr on June 6, perpetrators were armed with an assault rifle and a grenade launcher, and may have used a cell phone jammer to prevent the victims from calling for help.
When the van's security system prevented any money being taken, one of the offenders shot three times into the vehicle, although the occupants were not injured.
A similar attack then took place in Wolfsburg on December 28, officials said.
Officials said they believe the crimes were carried out to fund the suspects' lives on the run.
The three are also suspected of having carried out a 1993 bomb attack on a prison in Weiterstadt in Hesse, and a similar robbery, armed with a bazooka, on a security van in the town of Duisburg in 1999.
Deadly left-wing radicals
Since its formation in 1970, the Red Army Faction, an "urban guerrilla" organization that formed links with Palestinian militant groups, has been responsible for dozens of deaths.
Staub, Garweg and Klette are members of the so-called third generation of the group, which continued its violent attacks throughout the 1980s and early 1990s. During this period, it carried out assassinations of a number of prominent German executives.
By then, however, the Red Army Faction was a far cry from the disruptive force of its 1970s heyday when its activities caused a national crisis in Germany.
In a statement, police said Staub had a "lack of dental hygiene," while Garweg was described as having a "big nose" and "pointy face."
A reward of 20,000 euros ($22,276) is being offered for their capture.
Police have warned the three could be armed and should not be approached.