Tarek Obaid and Patrick Mahony will plead not guilty, their lawyers have indicated.
They are accused by Swiss state prosecutors of involvement in a vast embezzlement operation orchestrated by Jho Low, an advisor to former Malaysian prime minister Najib Razak, with the complicity of the latter.
The 1MDB scandal has led to criminal investigations around the world, including in the United States, Switzerland and Singapore.
It is alleged that billions of dollars were pilfered from the fund, officially 1Malaysia Development Berhad, by a number of people and used to buy items ranging from artwork to a super yacht.
Former Malaysian premier Najib was sentenced in 2022 to 12 years in jail for offenses linked to the misuse of public money in the 1MDB financial scandal. In February, his sentence was halved to six years.
Three judges
The latest trial, which is due to last throughout April, is being held at the Federal Criminal Court of Switzerland in the southern city of Bellinzona.
The case is being heard by three judges.
Lawyers for one of the accused on Tuesday asked for the president of the court to recuse himself from the case, believing that the judge had accepted the prosecution's thesis, and thereby cast into doubt his ability to conduct proceedings impartially, Switzerland's Keystone-ATS domestic news agency reported.
According to the original indictment, "the two accused are alleged, with the aim of enriching themselves and others, to have misappropriated at least $1.8 billion", transferred by 1MDB in connection with a joint venture with the Saudi oil exploration and production company PetroSaudi, "and then to have laundered the amounts involved".
"The allegations cover a period at least from 2009 to 2015 and constitute the offenses of fraud on a commercial basis, aggravated criminal mismanagement, and aggravated money laundering."
Obaid is a Swiss-Saudi dual national, while Mahony is a Swiss-British dual national.
'Lavish lifestyle'
"The two accused used money misappropriated from 1MDB to acquire, among other assets, real estate in Switzerland and in London, jewellery, private equity, to develop PetroSaudi activities from which they received substantial income, and to maintain a lavish lifestyle," the indictment said.
The Swiss public prosecution bureau thanked their counterparts in the United States, Malaysia, Britain, Singapore, Jersey, Canada and Barbados for their cooperation.
According to Mahony's lawyers Maurice Harari and Laurent Baeriswyl, quoted in the Tribune de Geneve newspaper, the "verbose indictment... is the culmination of a totally biased and incomplete investigation".
In 2005, Obaid served as a private advisor to the Saudi monarchy, the Swiss newspaper Le Temps wrote in a long investigation published in 2018.
PetroSaudi was based within the royal palace and the implicit guarantee of the crown opened doors in the oil world.
In 2009, Obaid approached Najib, who became Malaysia's prime minister that year, and the premier then offered Najib a business deal.
The 1MDB scandal led to the fall of Najib's government in 2018.