Australians Terry Pilkadaris and Matthew Griffin, Dutchman Guido van der Valk and Malaysian Anis Helmi Hassan brought the case against the Asian Tour after they were suspended for refusing to pay a $5,000 fine imposed for playing on a rival circuit.
Griffin played in the Chengdu Open, Maekyung Open, SK Telekom Open and Indonesian Open on the OneAsia Tour between April and July 2010, with Pilkadaris playing in three of the events, Van der Valk two and Anis just in Indonesia.
The Asian Tour said previously that they were simply following their rules and regulations in suspending the quartet for failing to pay, adding that other Asian Tour members had agreed to pay and gone on to play rival events.
The golfers had applied for an injunction so they could carry on playing and avoid paying the fines before the case was heard, but the Singapore judge rejected their application in late 2010 and they paid up.
Pilkadaris, Griffin and Hassan have since dropped their membership of the Asian Tour.
Lawyers for the four golfers will be allowed to cross examine Han and his co-defendant's in the hearing which begins on Wednesday at the Singapore High Court and is expected to last three days.
The judge will then review the case with a verdict to be given later this year.
Pilkadaris, 38, is a three-times winner on the Asian Tour and last played on the circuit at the 2010 Selangor Masters in Malaysia. His world ranking is 530.
He and the other three plaintiffs argue that the penalty is unfair and they should be free to play on whichever Tour they wish without paying large fines.
Pilkadaris, who earned $98,296 from the Asian Tour in 2009, said it cost him $1,000-2,000 in airfares, $400-1,000 in accommodation, $1,000 for a caddy and $400 for food and car hire to play each week in continental events.
"Whilst it costs me several thousands of dollars to travel each week, it is often four times this a week to travel with my wife and children," he told Reuters.
"Keeping in mind I only have a chance to earn money each week this becomes a very expensive sport to play. Most players ranked outside the top 100 in the world do not have sponsorship so all of these expenses are paid by the players."
The Asian Tour, who raised the fine to $10,000 at the start of this year, told Reuters they would not comment on the ongoing case.
Griffin, 28, won his first PGA Tour of Australasia event in September at the South Pacific Open and his world ranking is 733.
While the two Australians have not played on the Asian Tour since the row, Van der Valk has continued and was an impressive tied sixth at the season-ending Thailand Golf Championship in December, won by world number three Lee Westwood.
He has a ranking of 463 while 27-year-old Hassan, who turned professional in 2005, mainly plays on the lesser Malaysian Tour.
While it is the players that have brought the suit, the case adds to the rivalry between the Asian Tour and OneAsia Tour, which launched in 2009.
Han's organisation, which has 26 confirmed events for 2012, have accused their rivals of stealing their events.
The OneAsia Tour, now boasting 14 events with a combined prize money of over $16 million for 2012, denies the claims.