EXCLUSIVE: In the latest chapter of the gunrunning scandal known as Operation Fast and Furious, federal officials won't say how two suspects obtained more than 360 weapons despite criminal records that should have prevented them from buying even one gun.

Under current federal law, people with felony convictions are not permitted to buy weapons, and those with felony arrests are typically flagged while the FBI conducts a thorough background check.

However, according to court records reviewed by Fox News, two of the 20 defendants indicted in the Fast and Furious investigation have felony convictions and criminal backgrounds that experts say, at the very least, should have delayed them buying a single firearm. Instead, the duo bought dozens of guns on multiple occasions while federal officials watched on closed-circuit cameras.

Congressional and law-enforcement sources say the situation suggests the FBI, which operates the National Instant Criminal Background Check System, knowingly allowed the purchases to go forward after consulting with the Bureau of Alcohol, Tobacco, Firearms and Explosives, which initiated Operation Fast and Furious.

Under the failed anti-gun trafficking program, straw buyers -- those who legally purchase guns and illegally sell them to a third party -- were allowed to buy guns, many of which were sold to Mexican drug cartel members and subsequently lost. Related to the case, the U.S. government in May charged Manuel Osorio-Arellanes with killing Border Patrol Agent Brian Terry last year using a gun purchased through the program.

Court documents show the breakdown involves suspects Jacob Wayne Chambers, 21, and Sean Christopher Stewart, 28, both of Phoenix. Police arrested Chambers for felony burglary and trafficking stolen property in 2008, a year before he began buying more than 70 guns that ended up in the hands of the Sinaloa cartel. Stewart pled guilty to resisting arrest and criminal damage in 2001 and was arrested on drug charges in 2010. He was also charged with violating an order of protection and a local municipal court issued a warrant for his arrest. Stewart purchased 290 weapons.

Click here for more on straw buyers.

"You cannot sanction the violation of federal law by enabling or co-enabling prohibited persons, which includes felony convictions, from purchasing firearms," said Rep. Trey Gowdy, R-S.C., a former federal prosecutor and a member of the House Government Oversight and Reform Committee, which is investigating the botched ATF operation. Gowdy said he would discuss the apparent violation with committee chairman, Rep. Darrell Issa, R-Calif.

When asked about the breakdown, Stephen Fischer, a spokesman for the NICS System, said the FBI had no comment. However, an ATF agent who worked on the Fast and Furious investigation, told Fox News that NICS officials called the ATF in Phoenix whenever their suspects tried to buy a gun. That conversation typically led to a green light for the buyers, when it should have stopped them.

The apparent corruption of the system concerns Gowdy. "It is unconscionable and goes beyond just being a terribly ill-conceived investigation to bordering, if not crossing, into criminal activity," he said.

The investigation into why these men were able to purchase weapons and this sting operation gone wrong continues on Tuesday. The House Oversight Committee will hold a third hearing, focusing on what was happening on the other side of the border in Mexico.

The former and current ATF attachés to Mexico will testify that their agency never informed them of this operation.

Issa and his colleagues will also have their first opportunity to question ATF supervisors who have defended Operation Fast and Furious and the Justice Department's decisions to committee investigators.