Voters in Colorado are going to the polls to choose party candidates for November's mid-term elections.
The Democratic race for Senate nominee has garnered national interest due to high-profile endorsements.
President Barack Obama is backing incumbent Senator Michael Bennet, while former President Bill Clinton has endorsed rival Andrew Romanoff.
Primaries are also taking place in Connecticut and Minnesota, along with a Republican run-off vote in Georgia.
Some analysts are viewing the Colorado race as a test of Mr Obama's influence with middle-class voters.
Mr Bennet's candidacy has some problems of its own though.
The New York Times recently reported that, when he was a schools superintendent, Mr Bennet recommended a bad financial deal that cost the Denver public school system millions of dollars, while netting handsome profits for Wall Street.
The race remains close, with the latest poll showing Mr Bennet holding a slight lead.
In Connecticut, the retirement of long-serving Senator Chris Dodd has created a vacancy in a seat that Democrats have held since 1963.
Connecticut voters will choose the Republican candidate to stand for that seat on Tuesday. Democrats elected their candidate, Richard Blumenthal, in May.
The latest polls show Mr Blumenthal trailing the probable Republican candidate, Linda McMahon, an independently wealthy former wrestler and co-founder of World Wrestling Entertainment (WWE, formerly known as World Wrestling Federation or WWF)
In the Democratic contest for the governor's nomination, the man who ousted Senator Joe Lieberman from the Democratic ballot in 2006, Ned Lamont, will face the mayor of Stamford, Dan Malloy.
In Georgia, the Republican party is holding a run-off election for governor, after no candidate gained the requisite 50% in the initial primary.
Two candidates - Karen Handel and Nathan Deal - will compete in the run-off. Former Alaska Governor Sarah Palin is a strong supporter of Ms Handel, and campaigned with her in Atlanta on Monday.
Ms Palin has anointed Ms Handel as one of her "mama grizzlies", a term she coined for women candidates she considers formidable and who are "watching what is going on that is adversely affecting our cubs, our children, the future of America".
Ms Handel, who was also endorsed by former Republican presidential candidate Mitt Romney, now has a slight edge in polls.
Voters in Minnesota will also vote in primaries on Tuesday.