Republicans held on to key Senate seats in Indiana and Florida on Tuesday as they sought to hold off the Democrats' bid to retake the Senate majority.

But Democrats grabbed a Republican-held seat in Illinois in a race that has been described as a "coin flip" between the two parties.

The main focus of US and world media has been on the brutal race for the White House between the Republican nominee Donald Trump and Democratic candidate Hillary Clinton.

However, the importance of the races for the Senate and House of Representatives, which together make up the US Congress, cannot be underestimated.

Historically, Presidents have always struggled to pass their agenda while contending with an opposition-run House and Senate.

Republicans hold a majority of 54 to 46 in the Senate, which means Democrats need to pick up just four seats to take the majority if Ms Clinton wins the White House.

Some observers have suggested the possibility of a hung Senate providing the Vice President, either Republican Mike Pence or Democrat Tim Kaine, with the deciding vote.

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With several other races too close to call, control of the Senate depended on outcomes in North Carolina, Missouri, New Hampshire and elsewhere as the night wore on.

In Indiana, Republican representative Todd Young beat former Democratic senator and governor Evan Bayh, who had mounted a loud comeback bid, but wilted under scrutiny.

And in Florida, former presidential hopeful Marco Rubio beat Democratic rival Patrick Murphy, giving Mr Rubio a platform from which he could mount another bid for president in 2020.

The outcome was not unexpected since Murphy had been abandoned by his own party in the final weeks of the campaign, but polls had tightened heading into election day.

Election forecast blog FiveThirtyEight, run by pollster Nate Silver, gave the Democrats 50.7 per cent chance of winning control of the Senate compared to 49.3 per cent for the Republicans on Tuesday evening.

However, a FiveThirtyEight post yesterday said the fight for Senate control "remains basically a coin flip" and suggested the Republicans might ultimately maintain their majority.

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The Republicans retook the Senate majority just two years ago and even though control of the Senate is likely to be razor-thin whichever party ends up on top, the advantages of being in the majority are significant.

The controlling party holds the committee chairmanships, sets the legislative agenda and runs investigations. First up is likely to be a nominee to fill the vacancy on the Supreme Court.