Fine Gael's Mairead McGuinness has been elected to the European Parliament on the first count in the East constituency.
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Ms McGuinness topped the poll with 110,366 votes, exceeding the quota which stood at 107,313.
Labour's Nessa Childers is second with 78,338 votes.
Fine Gael Senator John Paul Phelan has polled well with 61,851 votes. But he was still behind the sitting MEP, Liam Aylward, who had 74,666 votes.
The second count in the North West constituency has been halted as discussions take place between the Libertas candidate Declan Ganley and Returning Officer Kieran McDermott, over the way ballot boxes were opened at the count centre this morning.
Mr Ganley asked to talk to the returning officer immediately after the announcement of the first count, with a view to clarifying issues of traceability and accountability.
Independent Marian Harkin topped the poll with 84,813 votes on the first count.
Mr Ganley polled in fourth place with 70,638. Fianna Fáil's Pat the Cope Gallagher was second with 82,643 votes and Fine Gael's Jim Higgins got 80,093.
The quota in the North West is 123,815.
Elsewhere, there is a recount in the Dublin constituency following a request from the Green Party candidate, Déirdre de Búrca.
Ms de Búrca is not in the running for a seat, but the result of the recount could put her in a position to reclaim some of her election expenses.
As expected Gay Mitchell topped the poll on the first count with 96.715 votes, followed by Proinsias de Rossa with 83,471 votes.
The third seat will be between Eoin Ryan (55,346), Joe Higgins (50,510) and Mary Lou McDonald (47,928).
The quota in Dublin is 101,658.
In the South constituency, Fianna Fáil's Brian Crowley has topped the poll with over 118,000 votes but has failed to reach the quota which is 124,532.
Fine Gael's Seán Kelly is in second place with 92,500 votes.
The count has been adjourned for the night after the second count with Toireasa Ferris (SF), Kathy Sinnott, (Ind) and Alan Kelly (Lab) battling it out for the last seat.
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More than half a million people are estimated to have voted, giving a turnout of just over 60% which is on a par with the European election turnout in 2004.
Watch this report from Prime Time which captured reaction as the election meltdown for Fianna Fáil unfolded
The panel discusses whether a general election should be called and if the results were a fundamental realignment