The Irish accountant and banker, Mr Des Traynor, and the Cayman Islands banker, Mr John Furze, were the two figures most involved in the running of the Ansbacher Deposits.
Mr Traynor died in 1994 and Mr Furze in 1997. Detailed records of the deposits are known to exist in the Cayman Islands but are subject to that jurisdiction's strict confidentiality laws. The identity of the Irish individuals who had money in the deposits remains a secret.
Two of the witnesses who have been called before today's sitting of the Moriarty Tribunal are known to have been intimately involved in at least some aspects of the running of the deposits. These witnesses are Ms Joan Williams and Mr Padraic Collery.
Ms Williams was Mr Traynor's long-term personal secretary and moved with him when he went from Guinness & Mahon bank to Cement Roadstone Ltd in the mid 1980s. She was an authorised signatory for at least some of the accounts.
In the early 1990s, when the "Ansbacher Deposits" were being moved from Guinness & Mahon Bank to Irish Intercontinental Bank, funds from the Ansbacher accounts were moved to accounts in the name of Hamilton Ross Ltd, a Cayman funds management company controlled by Mr Furze.
The authorised signatories for the Hamilton Ross accounts were Mr Traynor, Mr Furze, Ms Williams and Mr Collery. Accounts which held funds used to pay Mr Haughey's personal expenses and which had the code names S8 and S9, were among these accounts.
The McCracken Tribunal heard evidence about two companies, Kentford Securities Ltd and Amiens Investments, used by Mr Traynor when he was moving funds between accounts.
The tribunal was told that Mr Traynor would open accounts in Guinness & Mahon in the name of Amiens Investments for specific transactions, and close them again afterwards. The persons authorised to sign on behalf of Amiens Investments were Mr Traynor and Ms Williams. Kentford was operated in a similar manner, the McCracken tribunal was told.
Mr Collery is a banker and computer expert who was involved in assisting Mr Traynor in the operation of the Ansbacher Deposits. When Mr Traynor died, Mr Collery took over some of his work in relation to the accounts.
Why exactly the tribunal wants to question Mr Collery and Ms Williams about the identities of the Irish residents who kept funds in the coded deposits, is unclear. It is not known if the tribunal has evidence which shows funds being transferred from other Ansbacher accounts, into Mr Haughey's. If that is the case, then the tribunal will want to identify the owners of those accounts.
The tribunal has said that, subject to representations, it intends to hold today's cross examinations in private. Mr Frank Clarke SC is due to seek representation as counsel for the public interest and may make a representation in relation to the witnesses being questioned in private session.
Mr Justice Moriarty is to make a public comment on the tribunal's terms of reference. It is not expected that today's hearing will continue into Friday.
