Voters in five north-eastern American states are casting ballots in primaries that are expected to extend the leads of the two presidential frontrunners.
The latest polls had Donald Trump and Hillary Clinton ahead in all five states for their respective parties.
Pennsylvania, Connecticut, Rhode Island, Delaware and Maryland, have a total of 118 pledged delegates at stake.
A bump for Trump? - Republican contest
But Mr Trump's rivals Ted Cruz and John Kasich have already shifted focus away from the north-east to the Indiana, Oregon and New Mexico primaries.
The pair agreed this week to co-ordinate strategies to try to stop Mr Trump winning more state primaries, a move Mr Trump condemned as a sign of weakness and desperation.
All five states were expected to continue Mr Trump's lead but a complicated contest in Pennsylvania, the day's biggest prize, was expected to test his recently reorganized campaign.
The state features the sort of complex rules Mr Trump has repeatedly slammed for being "rigged" and which forced him this month to reshuffle his team.
Just 17 of the 71 Republican delegates up for grabs in Pennsylvania on Tuesday are allocated to the candidate who wins its primary. The other 54 delegates - elected directly by voters - are free agents able to support anyone they choose at the Republican National Convention in July.
"It's as crooked almost as Hillary Clinton," Trump said on Monday at a campaign event in West Chester.
It would be difficult to predict which Republican candidate would get the most support from Pennsylvania.
Many delegates said they would vote for whoever wins the state or their district, at least on the first ballot at the convention.
If those delegates held to their informal promises, Mr Trump could win most of Pennsylvania's votes on the first round in Cleveland, conservative strategist Charles Gerow, who was also running to be a Pennsylvania delegate, said.
While Mr Trump had a clear lead in party delegates, there was still a chance he could fall short of the 1237 needed to win the Republican nomination outright.
If he did not reach that figure, the vote would go to a contested convention where delegates would be free to change which candidate they were backing. A different nominee like Mr Cruz or Mr Kasich could then emerge.
Clinton clincher? - Democrats
Mr Trump and Mrs Clinton took commanding wins in their home state of New York a week ago, breaking some momentum gained by their rivals Mr Cruz and Vermont senator Bernie Sanders.
Mr Sanders, who had won seven of the eight states before New York, insisted he stood a good chance to win some of the states.
"I think we've got a path to victory and we're going to fight this until the last vote is cast," Sanders said on CNN.
Mr Sanders was pushing hard for a win in Rhode Island, where Mrs Clinton's lead is slimmer. He was also hoping for an upset in Pennsylvania, with its many working-class voters.
However, after Tuesday's results, it would be unlikely for Mr Sanders to overcome Mrs Clinton's lead to become the Democratic nominee for president.
With a large African-American population and one of the highest average household incomes in the country, Maryland represented a daunting challenge for the Sanders campaign.
Pennsylvania seemed like more fertile ground for Mr Sanders because it looks somewhat like Michigan, a blue-collar state that his campaign won. However, polls showed Mr Sanders trailing badly even in Pennsylvania.
If Mrs Clinton won convincingly, it seems likely Mr Sanders will shift his focus from competing outright with her to trying to push the Democratic Party platform further to the left.
If he does well in coming primaries like California and New Jersey, he will have more leverage.
In the Republican delegate race for 1237, Mr Trump has 845 delegates, Mr Cruz 559 and Mr Kasich 148.
The Democrats are racing fror 2383 delegates, with 1428 pledged to Mrs Clinton and 1192 to Mr Sanders. However, there were also 557 "super-delegates" whose votes were not based on state results and could support whoever they chose at the democratic convention in July.
Of those, 518 were supporting Mrs Clinton, leaving 39 for Mr Sanders. That would bring Mrs Clinton's lead to 1946 compared to Mr Sanders' 1192.
- BBC / Reuters