Sen. Hillary Clinton has won Ohio and is projected to take Texas, but still trails Sen. Barack Obama in overall delegate support, while Sen. John McCain has won the Republican nomination.
Obama cruised to an early victory Tuesday night in Vermont, but Clinton later fought back with a strong win in Rhode Island.
In Ohio, with roughly 87 per cent of polls reporting, Clinton was leading or had won 55 per cent of the delegates, while Obama had 43 per cent. There were 164 delegates up for grabs.
"Thank you, Ohio!" Clinton told a cheering crowd in Columbus. "For everyone who has ever been counted out but refused to be knocked out, for everyone who has stumbled but stood right back up, and for everyone who works hard and never gives up, this one is for you."
Texas had both a primary and caucuses on Tuesday. Of the state's 228 delegates, 126 were to be decided through the night's primary and 67 through the caucuses.
By late evening, Clinton had barely edged ahead of Obama in the primary. With 76 per cent of polls reporting, Clinton had 51 per cent support while Obama had 47 per cent -- enough to be named the projected winner.
Because delegates are awarded proportionally based on the popular outcome of a state, Clinton was unable to surpass Obama in total delegate support.
Various news agencies and the campaigns themselves have differing numbers when it comes to the exact number of delegates Obama and Clinton have to date. But most had Obama ahead by more than 100 delegates before Tuesday. The Associated Press reported that he had 1,386 delegates, including party-chosen superdelegates. Clinton had 1,276.
Obama, speaking to supporters in San Antonio, Texas, said that despite Clinton's victories Tuesday night he would still be in the lead.
"No matter what happens tonight, we have almost the same delegate lead as we did this morning, and we are on our way to winning this nomination," he said.
Earlier Tuesday, Clinton had suggested she would stay in the race if she won Ohio.
"You don't get to the White House as a Democrat without winning Ohio," Clinton said.
"My husband didn't get the nomination wrapped up until June (in 1992). That has been the tradition," she said. Clinton didn't mention that this year's primary cycle began much earlier than in 1992.
McCain wins nomination
While Obama and Clinton fought to take a decisive lead, Sen. John McCain secured his party's nomination. U.S. President George Bush is expected to endorse McCain on Wednesday.
McCain needed 1,191 delegates to become the Republican candidate. He now has at least 1,205 after winning Ohio, Vermont, Texas and Rhode Island.
"My friends, now we begin the most important part of our campaign," he told supporters Dallas. "We must make a respectful, determined and convincing case to the American people that my election as president ... is in the best interest of the country we love."
His main rival, former Arkansas governor Mike Huckabee, phoned McCain late Tuesday to concede defeat.
"I have extended to him not only my congratulations, but my commitment to him and to the party to do everything possible to unite our party, and more importantly, to unite our country," Huckabee told supporters at a rally in Irving, Texas.
Huckabee went on to call McCain an "honourable man" who had run an "honourable campaign."
McCain almost saw his campaign collapse last summer and then he placed fourth in the Iowa caucuses. But he forged ahead and won New Hampshire, then continued with a streak of victories in January and February.
