The High Court has rejected two applications to bring petitions challenging the result of the same-sex marriage referendum.

Gerry Walshe from Lisdeen Road in Co Clare and Maurice J Lyons from Callan in Co Kilkenny had brought separate applications to the High Court.

High Court President Mr Justice Nicholas Kearns ruled that the amendment to the Constitution was very significant and was not a technical amendment.

He said the test for being allowed to bring a petition to challenge the result of a constitutional referendum was whether or not the conduct being alleged had "materially affected" the outcome of the referendum.

Justice Kearns said this was a higher test than an ordinary judicial review challenge to legislation.

He ruled that he did not find any grounds in relation to Mr Walshe's case or Mr Lyons' case that would persuade him to grant permission to them to bring petitions.

In relation to Mr Lyons' case, Mr Justice Kearns said it was not the court's function to trespass on the will of the people who gave the proposal significant and substantial approval by commenting on the correctness of their decision.

Both men represented themselves in court.

Mr Justice Kearns also dismissed a submission by Mr Lyons that those who had not voted should be treated as having voted no.

He found no significant point of law had been raised in the challenge. He awarded costs against both men.

He added that challenges like this should not be undertaken lightly, having regard to the very clear view of the people.

Earlier, Mr Walshe had said his challenge was not an "anti-gay issue". He said it was a failure of fair procedures in the referendum process.

He said there was a lack of impartiality in the promotion of the Yes campaign and the people of Ireland had been denied a fair, equal and impartial referendum.

He also said posters promoting a Yes vote were seven to ten times more frequent than no posters.

He said in three different supermarkets in Co Clare there were nine posters - six of which were clearly identifiable as from Labour and Fine Gael.

He said the political parties were servants or agents of the Government and funds had been used to promote the posters.

He also said full copies of the proposed referendum bill had not been made available to post offices before the vote on 22 May.

Mr Justice Kearns said this was no longer a requirement as legislation had been enacted subsequently to repeal this requirement.

He also said the marking of ballot papers with identification numbers or serial numbers compromised the secrecy of the ballot.

He said CCTV could identify voters through the serial numbers.