Hillary Clinton and Barack Obama head into their next showdown in Nevada tomorrow amid allegations of strong-arm tactics on the Las Vegas Strip, dishonest campaign ads, and with race again looming as a significant issue.

Voters in South Carolina, meanwhile, have their say in the highly volatile Republican race. It is a contest that is far from settled and where the leading candidates are already plotting their course to February 5, "Super Tuesday", when more than 20 states vote nationwide in a delegate-rich battle that could settle both parties' nominations.

In Nevada, Mrs Clinton and Mr Obama were accused of distorting each others' records, with Mr Obama rolling out a new routine at a Las vegas rally on Thursday night in which, using humour, he repeatedly attacked Mrs Clinton by name for being duplicitous and not "saying what she means".

As they campaigned across the Silver State for the final time, the Democratic rivals were also looking ahead, to their next contest in South Carolina on January 26, and like the Republicans, to Super Tuesday, a day that will cost their campaigns tens of millions of dollars.

Aides to Mr Obama held a conference call with donors and strategists to discuss the February 5 contests in Missouri, Tennessee, Connecticut and New Mexico. Mrs Clinton's camp was negotiating for television advertising spots in multiple Super Tuesday states, with both already on the air in California, the biggest prize on that day.

A new poll by Nevada's biggest newspaper shows Mrs Clinton nine points ahead of her rival, 41 per cent to 32. Polling caucus goers is notoriously difficult, but the survey strongly suggests that Mr Obama, as a black man, is struggling to win over Hispanics in Nevada, despite his endorsement by the heavily Latino Culinary Workers Union. It is the state's biggest and most powerful trade organisation and has particular clout in Las Vegas's casinos.

African Americans and Hispanics have had an antagonistic and uneasy relationship, particularly as they have competed for jobs in the big cities. In the poll, Mrs Clinton enjoyed strong support among Latinos, and among women and traditional Democrats - a trend reflected nationally and one she hopes will serve her well on February 5.

On Thursday a Nevada judge blocked a lawsuit by a union with links to Mrs Clinton, and ruled that nine Las Vegas casinos could open caucus sites, so that casino employees do not have to leave work to vote. The move should aid Mr Obama, as most casino workers belong to the big union that has endorsed him.

But there were growing reports that the union was struggling to keep many of its Hispanic members in line, and rumours of increasing pressure being applied to get them to vote for Mr Obama. A union backing Mr Obama then ran a radio advertisement in Spanish accusing Mrs Clinton of being "shameless" for trying to disenfranchise Latino voters with the lawsuit.

"Hillary Clinton does not respect our people," it said. The Clinton campaign fiercely denied being behind the legal attempt to shut down the casino caucus sites. "It’s pathetic and it's sad and it's unfortunate that they have to stoop so low," said Dolores Huerta, an Hispanic labour leader who supports Clinton, in reference to the radio ad. "I have yet to find even one worker — a Latino worker — who is supporting Barack Obama."

In South Carolina, the candidates are facing a Republican electorate so fractured that none can rely solely on their core constituency in the state to bring victory and are trying to widen their appeal. John McCain and Mike Huckabee are locked in a fight for first place. After their respective wins in Iowa and New Hampshire, victory in the Palmetto State would give one significant momentum heading into Florida on January 29 and then onto Super Tuesday. The latest poll has them in a statistical tie - Mr McCain with 27 per cent support, Mr Huckabee with 25 - with Mitt Romney on 15 per cent.

Mr McCain, who enjoys strong support among veterans, has also been appealing to values voters, touting his consistent opposition to abortion. Mr Huckabee, backed by evangelicals, is playing on recession fears with a message of economic populism. Mitt Romney, who revived his campaign with victory in Michigan, is focusing on picking up delegates in Nevada's Republican vote tomorrow, a contest largely ignored by his rivals, and then onto the February 5 contests.

Rudy Giuliani is banking all on victory in Florida, which he hopes will propel him into Super Tuesday. Fred Thompson, the former senator and Law & Order star, has to win South Carolina if his campaign isn't to founder, but appears to be struggling.

Times Recommends

• Henning Mankell: ‘If Wallander was alive, I wouldn’t be a friend of his’
• Secret society's skull and crossbones for sale
• Nigerian leader vanishes after medical treatment