In a letter released today, the laureates say the 14 minority Shiites were convicted in a mass trial and sentenced "based on the actions of the worst defendant."
They also allege that Saudi authorities coerced confessions and subjected the arrested protesters to physical force.
Among those facing execution is Mujtaba al-Sweikat, who was heading to the United States to attend Western Michigan University.
The American Federation of Teachers has urged President Donald Trump to demand that Saudi Arabia halt the executions of al-Sweikat and the others.
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