CIÉ workers today staged a "no fares" protest that is expected to cost the company up to €1.1 million in lost revenue.
Passenger numbers were reported to have increased on some routes as a result of the action.
Travellers across the country were not asked to pay fares on buses and trains in the protest at plans to break up the company by the Minister for Transport.
Services at Bus Éireann, Iarnród Éireann, and Dublin Bus have run to schedule according to reports.
It had been feared the action might cause widespread disruption if large numbers decided to take advantage of the fareless service, which may have resulted in overcrowding.
However so far the customary Friday afternoon rush has not been exacerbated by the action.
There have been no major disruptions to bus or rail services. However, a spokesperson for Iarnród Éireann said there was a "noticeable increase" in passenger numbers on some routes. Officials noticed an increase of about 10 per cent on Dublin-bound trains from Galway, Limerick, Sligo and Westport.
Earlier Iarnród Éireann warned travellers that ticket-holding passengers would be given priority with people being turned away if the trains were full.
A spokesman for Bus Éireann said there was not an excessive number of travellers availing of the "No Fares Day" and said passenger numbers were "nothing more than expected for this time of year".
Dublin Bus also said there were no problems being experienced on their routes in the capital.
CIÉ workers say further industrial action can be avoided if Mr Brennan agrees to reopen talks on his privatisation plans for public transport.
SIPTU national industrial secretary Mr Noel Dowling said "No Fares Day" was aimed at triggering a public debate about the merits of Mr Brennan's proposals rather than imposing a veto over them.
"All the Minister's stated objectives for improving public transport can be achieved without confrontation. All we are asking is that he engage with us constructively," said Mr Dowling.
A spokesman for the Minister said there were no definite plans for talks, although the privatisation plans might be raised in the context of a meeting this afternoon with ICTU and SIPTU at Government Buildings over the break-up of Aer Rianta.
Mr Brennan's plans include the franchising out of 25 per cent of Dublin's bus market to a private operator by next January.
The trade unions claim this will result in a public transport system similar to that in London - which Mr Hugh Geraghty, secretary of the CIÉ group of unions, described yesterday as a "model for disaster".
At a press conference in Dublin yesterday, the unions cited figures suggesting the cost of running public transport in the English capital would reach £1 billion sterling per year by 2006.
At present, more than 2,000 people were employed in bus regulation alone, while a trans-European study showed London fared worst on reliability, staff behaviour and safety and only mid-range on value for money, according to the unions.
Mr Liam Tobin, general secretary of the National Bus and Railworkers' Union, noted Dublin Bus received a State subvention worth 25 per cent of operating costs. This "compared with 31 per cent paid by the British taxpayer to the private-owned London transport model Mr Brennan favours.
"Instead of being obsessed with paring down subventions and squeezing extra revenue out of our predominantly low-income passengers, Mr Brennan should be embracing imaginative social objectives such as 'no' or 'low' fare initiatives that would persuade more commuters to leave their cars at home," Mr Tobin said.
He denied workers were trying to veto change and added: "We are conscious that that charge can be levelled at us but I don't think anybody would expect us to sit there and see our members' livelihoods be destroyed".
But the Dublin Chamber of Commerce criticised today's action, saying it "clearly demonstrated that the public transport market needs more operators".