Republicans are holding caucuses or primaries in four states, with Democrats voting for their candidate in three.
Former Secretary of State Hillary Clinton leads the Democrats’contest while billionaire Donald Trump is ahead in the Republicans’ race.
Efforts by Republicans to slow Mr Trump’s march have so far failed.
At a televised debate on Thursday, his main rivals for the nomination, Ted Cruz and Marco Rubio, launched a series of attacks on him.
Mitt Romney, the 2012 Republican nominee, earlier accused the businessman of bullying, greed and misogyny. Mr Trump dismissed Mr Romney as a “failed candidate”.
Two days earlier, on Super Tuesday, Mr Trump won seven of the 11 contests.
The more states pick him, the more delegates he claims. Republican candidates need 1,237 delegates to win the nomination.
Mr Trump is 908 delegates short; 155 are available on Saturday.
But polls have already closed in Kansas, with Mr Cruz taking an early lead as the first votes are counted.
In a number of states, the evangelical vote could prove decisive, with Mr Trump managing to draw some support from a base more usually associated with Mr Cruz.
On Friday, Ben Carson, who was at one point a Republican front-runner, dropped out of the race.
Democrats are voting in caucuses in Kansas and Nebraska, as well as in a primary in Louisiana.
Mrs. Clinton heads the race and has in recent days started targeting Mr Trump in her speeches instead of her fellow Democratic candidate Bernie Sanders.
Opinion polls suggest she has strong support in Louisiana among black voters but analysts say the race between Mrs Clinton and Mr Sanders may be close in other states on Saturday.
One-hundred-and-nine delegates are available in the Democrat races on Saturday. Mrs Clinton needs a further 1,137 delegates to win the nomination.
The election itself, on 8 November, will see America vote for a successor to Barack Obama, a Democratic president standing down after two terms in office which have seen the Republicans take control of both houses of Congress.
