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President Donald Trump has claimed victory for the Republican candidate in the election for a House seat in Ohio.
But US media said the race was still too close to call, in a seat long held by the Republicans.
The election is seen as a key indicator ahead of November's mid-terms.
Tuesday also saw four states hold primaries to choose candidates for the mid-terms. It appears women will have a record number of nominees for both the House and governorship contests.
What has happened in Ohio?
Republican candidate Troy Balderson has been taking on Democrat Danny O'Connor in Ohio for a seat in the US House of Representatives. Ohio is one of the key battleground states in the mid-terms.
Mr Trump tweeted "Congratulations to Troy Balderson on a great win in Ohio. A very special and important race!"
But US news outlets have not called the contest yet. The New York Times gave Mr Balderson 50.2%, a lead of 1,754 votes in the 12th Congressional District race, with all precincts reporting. But at least 3,367 provisional ballots are still outstanding, which could lead Mr O'Connor to force a recount. He said: "We're not stopping now."
A provisional ballot is used to record a vote when there are questions about a voter's eligibility.
The BBC correspondent in Washington says even if the Democrats lose the seat, they can claim a moral victory in Ohio, and will point to the results as further evidence that they are poised for success in November.
Democrat House representative Ben Ray Luján said the seat should have been a "slam dunk" for the Republicans and the closeness of the contest was an "ominous sign" for them in November.
Mr Trump won the 12th Congressional District in 2016 by more than 11 percentage points and Republicans have held it since 1983.
Mr Balderson and Mr O'Connor will have to fight the seat again in November.
What about the primaries?
Kansas, Michigan, Missouri and Washington state have all been choosing candidates for the mid-term elections.
It appears that all the Republican candidates so far called as winners have been endorsed by Mr Trump.
They include John James, an African-American Republican, who won the Senate race nomination in Michigan.
The Kansas gubernatorial election has been rancorous for Republicans. The New York Times says it appears Mr Trump's pick, the hard-right Kris Kobach, may have upset incumbent Jeff Colyer.
In Missouri, Democrat senator Claire McCaskill will take on the Trump-backed attorney general Josh Hawley in the Senate race.
Former Democratic Party legislative leader Gretchen Whitmer will face off in the Michigan gubernatorial race against Trump ally Bill Schuette.
A breakthrough for women
The Center for American Women and Politics (CAWP) said a record had been set for women major party nominees for US House elections in any one year.
At least 168 have been nominated, with possibly more to come.
The CAWP said 11 women had also been chosen as their party's nominee for governor, surpassing the record of 10 in 1994.
Indeed, Ms Whitmer could lead an all-female Democratic state-wide ticket in Michigan against Mr Schuette.
Laura Kelly will have a tough battle in the Republican stronghold of Kansas, but if she faces Mr Kobach she could play on his extremist profile to target centrist Republicans.
Michigan - another key battleground - also saw a swathe of women nominees.
Democratic women could outnumber white male colleagues in the House after November, a recent study suggested.
Estes vs Estes
And one interesting sidebar: Ron Estes has beaten Ron Estes in a Kansas Republican primary.
The victorious incumbent congressman had to fund a campaign to spell out which candidate was which. The beaten candidate was Ron M Estes - his opponent said the M stood for misleading.
The beaten man's campaign was described by some analysts as "not serious".
The winning Ron Estes took about 80% of the vote and will face Democrat James Thompson, a supporter of Bernie Sanders in November.
What's up for election in November?
All 435 House seats, 35 of the 100 Senate seats and 36 of 50 governor races are to be fought.
The Democrats need to pick up 23 seats in the House to gain a majority.
With dozens of Republican lawmakers retiring this year, the minority party has a decent chance of taking over the House.
In the Senate they need just two seats to take control. But the Republicans are tipped to retain their majority and perhaps even consolidate it.
A general opinion poll of voting intentions last Friday suggested Democrats were 6.1 percentage points ahead of Republicans.