There were reports last night that some people who wished to vote at polling stations in south and west Belfast were turned away because stations were overwhelmed by the high turnout.
Press Association reported voters were disappointed at polling stations in Knock breda and Poleglass.
Queues were also reported in West Tyrone, North Down and Mid Ulster.
Sinn Fein's Mr Mitchel McLaugh in, said the fact that the Westminster and local elections took place simultaneously caused the delays.
There was a real risk "that many people may be disenfranchised because not sufficient resources were allocated to this election", he said.
Northern Ireland's Chief Electoral Office, Mr Dennis Stanley, acknowledged his office had received several reports of queues but said he was bound by strict electoral rules.
"The law is quite clear on this. Only those people with ballot papers at 10 p.m. can cast their votes before the polls close," he said.
In West Tyrone, both the SDLP and Sinn Fein reported record turnouts in Omagh and Strabane.