The Broadcasting Complaints Commission has upheld eight complaints against RTE's The Late Late Show broadcast on the 24 October, which featured comedian Tommy Tiernan in an interview with Gerry Ryan.
Mr Ryan was presenting the show because Pat Kenny was absent due to a familly bereavement.
Complaints were made by a number of individuals, including a mother of a person with Down's Syndrome, and by a representative of the group Pavee Point, which represents Travellers.
With regard to a joke which related to a person in the National Rehabilitaton Hospital in Dún Laoghaire, and mentioned Travellers in the punch line as well, the BCC noted that Mr Ryan actively engaged in the jokes being told by the comedian and in effect, urged him on irrespective of manner or content.
The BBC said that at no stage did Mr Ryan challenge or attempt to curb the presentation or what was being said by the comedian.
The BCC said that while accepting that humour can be irreverent and that freedom of speech is of paramount importance, the manner and content of the jokes about a disabled person and a Traveller went beyond acceptable standards.
In the joke based on disability, the mimicry and punch lines were likely to cause offence to regular viewers of the 'Late Late Show'.
With regard a joke featuring Travellers, the Commission found that not only did the content go beyond acceptable standards, it was derogatory of the Traveller Community.
The BCC described the joke as totally inappropriate.
In response, RTÉ has said it takes seriously all complaints upheld by the BCC and regrets if the item in question caused viewers undue offence.
The broadcaster said it recognises its responsibilities as the standard bearer in Irish broadcasting and takes great care to balance its responsibilities, alongside the need to entertain.
It is in this context that RTÉ programmes like The Late Late Show offer viewers in Ireland an opportunity to see all of Ireland's most popular comedians.
The broadcaster said it intends to continue that policy in the future, with renewed focus on the latest rulings and how they relate to the implementation of RTÉ's Code of Programme Standards.
It also said complaints about Tommy Tiernan on the Late Late were upheld in 2004 and full account was taken of them at the time.
No complaints have been upheld against him for the last four years.