The State Examinations Commission (SEC) has revealed Leaving Certificate results of 51 students have been withheld.
This is due to a suspicion of cheating.
This includes full results withheld, or marks withheld, from candidates found to be in breach of examination regulations.
The SEC has also provisionally withheld 20 other results, without prejudice, pending further communication with the schools and candidates concerned.
A decision to withhold a result or marks is open to appeal.
This is a drop in the number of withheld results compared to previous years.
In 2018, 72 Leaving Cert results were permanently withheld - while in 2017, that number dropped again to 57.
While exact details of the alleged breaches are unclear, the SEC says a candidate is liable to have their whole examination cancelled or be debarred from entering any of the State examinations for a number of reasons.
This includes bringing any books, notes, papers, mobile phone, electronic address book or data bank into the examination hall.
Regulations show this includes but is not limited to iPods, MP3 players - or any products with an electronic communication or storage device facility.
Candidates cannot be in possession of any such devices, whether they are switched on or not.
The most common penalty is the withholding of the result in a particular subject.
Where a more serious breach occurs, withholding of all results and/or debarring from repeating the examination may be applied.
The SEC adds: "Withholding of results occurs as a consequence of a candidate attempting to gain advantage in the examination by means which contravene the regulations for the conduct of candidates during examinations as set out in the Rules and Programmes for Secondary Schools."
Nearly 59,000 students received their results on Tuesday.