No Leas Cheann Comhairle has been elected despite votes for four candidates in the Dáil on Thursday.
Sinn Féin nominee Sean Crowe was defeated by 106 votes to 33.
Independent Mattie McGrath received 20 votes to 117 against.
Fianna Fáil candidate Pat 'The Cope' Gallagher was defeated by 83 to 52, while Fine Gael TD Bernard Durkan lost by 83 votes to 52.
After the inconclusive votes Ceann Comhairle Sean Ó Fearghaíl said the issue was now a matter for the party whips and they should treat it with “some urgency”.
A number of TDs spoke in favour of each candidate, including some of their non-political experience.
Sinn Féin leader Gerry Adams said Mr Crowe was a "very, very fine singer and may lighten the darkness of your evenings".
Independent Michael Healy Rae said Mr McGrath "does possess all-Ireland medals for dancing. While others can sing, our candidate can dance".
Fine Gael Kildare South TD Martin Heydon said of Mr Durkan: "I don't know if Bernard can sing, but he's certainly the best orator I know".
Fianna Fáil Galway East TD Anne Rabbitte praised Mr Gallagher's mentoring. She said he had "given his time" to assisting new TDs and would be a very fair Leas Cheann Comhairle.
