Democratic presidential candidate Bernie Sanders is hoping to keep his campaign alive with strong showings in the Kentucky and Oregon primaries.
Front-runner Hillary Clinton is almost certain to secure the nomination in July, with a significant delegate lead.
She has been campaigning in Kentucky, saying husband and former President Bill Clinton would take charge of revitalising the economy.
Both races could be fairly competitive, national polls predict.
Mrs Clinton has won 94% of delegates needed to win the nomination, a total of 24 states to Mr Sanders' 19.
Republicans will vote in Oregon on Tuesday, but that race is all but decided, with front-runner Donald Trump having pushed out all of his competitors.
The Kentucky Democratic primary will award 60 delegates to go to the party's convention in Philadelphia while Oregon's primary will award 74.
Kentucky's primary is closed, meaning only registered Democratic voters can participate.
In Oregon, voters cast ballots entirely by mail.
(BBC)