The Garda Representative Association (GRA) has claimed more than 20,000 motorists are waiting to have their licences endorsed with penalty points because the new scheme is not computerised.
GRA general secretary Mr P.J. Stone has accused the Government departments involved in the scheme of oneupmanship over "who is going to be next to introduce a penalty point".
The backlog which has now built up means gardaí at the Fines Office in Dublin are working hard to prevent the scheme from collapsing, he said.
"Some people seem to be under the illusion that the Garda staff associations are against the concept of penalty points, but nothing could be further from the truth. The Minister for Transport is getting a lot of praise for saving lives through this and we are not taking that away from him.
"We are simply trying to point out that there are problems with the system that need to be resolved. And we shouldn't be treated like anarchists for doing that.
"We believe the whole thing should be computerised, that there should be no need for paperwork at the side of the road when a motorist is stopped for speeding. And certainly no more offences should be introduced until the system is computerised."
Since last Thursday motorists who are detected driving without insurance will incur five points on their licences.
Next month the non-wearing of seat belts will be added to the list and around seven further offences are to be added in the next nine months, when the computerised system is due to be introduced.
The Department of Transport said the fact that more than 23,000 drivers have received points is an indication it is working. "And the number of deaths has dropped as a direct result of points," a spokeswoman said.
Since the introduction of penalty points last November there have been 51 fewer road fatalities compared with the previous corresponding period. However, in May road deaths jumped to 38, up from 20 in May 2002.
