The stakes were high for Republicans as Donald Trump hopes to gather the necessary momentum to become the party’s candidate in November elections and his four challengers led by Senators Marco Rubio and Ted Cruz hoping to stop the political outsider they say would tear apart the party.
Trump leads in all opinion polls except in Cruz’s home state of Texas.
Among Democrats, Hillary Rodham Clinton hopes to take firm control of a race that was once considered smooth sailing for her before Bernie Sanders nearly tied with her in Iowa and then defeated her by a large margin in New Hampshire before she steamrolled him in Saturday’s South Carolina primary.
Clinton is favoured over Sanders in most of the 11 states holding votes for the centre-left party. Opinion surveys showed Sanders leading in his home state of Vermont and narrowly behind Clinton in neighbouring Massachusetts.
Some 600 delegates, or about a quarter of those needed to secure the Republican nomination, are at stake, while about 1,000 are up for grabs among Democrats, some 20 per cent of the total.
Among Republicans, Texas is the biggest prize with some 155 delegates, followed by southern states Georgia, Tennessee and Alabama. On the Democratic side, the largest state is also Texas with 252 delegates, followed by Georgia and Massachusetts, with 116 each and Virginia with 110.
The first polls opened in the north-eastern state of Vermont at 5 am (1000 GMT) and the final polls were not due to close until 0500 GMT Wednesday in Alaska.
Voting will take place for both parties in Alabama, Arkansas, Colorado, Georgia, Massachusetts, Minnesota, Oklahoma, Tennessee, Texas, Vermont and Virginia. Republicans also vote in Alaska.