The Assessment and Qualifications Alliance claims the papers, for one of the three business studies modules, vanished in the post after being marked by a single examiner and sent to its offices.
At York college, one of three affected, managers say the AQA only admitted the problem at the last minute - too late to forewarn the students.
Margaret Price, acting director of teaching and learning at the college, said: "They must have known about the problems but failed to tell us until we had already found out we didn't have the results."
Student Madeline Taylor, 17, had been awaiting the results of her retake of the module.
She said: "I went into the room where we were going to get our results and one of the students said the test papers were missing.
"I couldn't believe it, then one of the lecturers gave me a copy of a letter and that was it. Everyone was really shocked and annoyed. There were a few tears. I cried when I got home."
The AQA says 209 students were affected. It claims the marked papers and the sheets recording the marks would have been sent separately by the examiner - meaning there would have been at least two postings.
Both of these, the AQA says, failed to arrive.
It refuses to identify the other two colleges, claiming it wants to protect their privacy.
Helen Hallett, an assistant director in charge of external relations at the AQA, said: "This is what we call a 'missing scripts case'. When we have missing scripts, we take account of the performance on other modules and estimate what the performance would have been.
"There are not a huge amount missing; 0.000539 per cent."
Madeline Taylor's father, Peter, a secondary-school teacher, said: "If I lost a piece of coursework I'd be for the high jump.
"It's a matter of professionalism. I think the students have a right to expect the same standards from the exam boards."