TEHRAN -- As negotiators work to finalize a deal over Iran's nuclear program, industries and consumers hit hard by U.S. sanctions are eager to feel the benefits of normalized relations. Among them are Iran's car enthusiasts.

Amir Bagheri's 1965 Mustang has an on-board turntable and plenty of juice. His is not your average ride on the roads of the Islamic Republic.

Bagheri says his love for cars runs so deep that his wife is sometimes jealous of the vehicles. He first fell head over heels in love with his dad's Mustang when he was just a kid.

Amir Bagheri drives his 1965 Mustang in Tehran CBS News

Now, a successful businessman, he owns several, including a rare Shelby Cobra. But U.S. sanctions have made parts for it -- and other American classics -- very hard to get hold of. Bagheri told us he frequents Ebay for parts and sometimes has to wait six months before receiving what he ordered.

For American classic car buffers in Iran, a political deal can't come soon enough. Before the Iranian Revolution in 1979, U.S. cars were popular here. Almost 40 years on, survivors are tucked away all over Tehran -- prized, polished and kept on the road by the members of Iran's Automobile Federation.

Of course they evoke powerful nostalgia for another era. Mojtaba Mirlatifi loves his vintage Barracuda but his heart belongs to a 1972 Chevy Chevelle. Four decades ago he had one just like it. It brings back happy memories of his time as a student in Fresno, California.

In 1959 President Eisenhower even rode with the then-Shah through Tehran in a Cadillac Eldorado, which has since been rescued by a collector.

Ramin Salehkhou stands with the Cadillac Eldorado he's restoring CBS News

Ramin Salehkhou, the head of the Iran Classic Car Committee, says the car will ride on the roads again.

"What would a restoration be if the car didn't run again?" said Salehkhou.

American classic cars -- stranded in Iran by history and politics -- are still king of the road.