The arbitration panel adjudicating on the relegations of Hearts and Partick Thistle got under way on Friday.
After a Court of Session hearing earlier this month, Lord Clark ruled that an independent tribunal should hear the case under Scottish FA rules.
The two clubs are challenging their relegations from the Premiership and Championship respectively after the season was curtailed early.
Both sides have selected a QC from an approved list, and agreed on a chair.
It is unclear how long it will take that three-strong panel to reach a decision.
However, given the weight of evidence to be considered, and the legal debates to be heard, it could be the week building up to the season starts on 1 August before a verdict is reached.
A further complication could be that the SPFL's agm is on Monday and the Scottish FA's later in the week - both of which could involve potential witnesses for the panel to hear from.
Dundee United, Raith Rovers and Cove Rangers - the respective champions of the Championship, League One and League Two - are fighting the Hearts and Thistle case.
United estimated the legal bill for the trio could "escalate to over £150,000",, external and two fans completed a walk on Saturday that has already raised around £40,000 of that potential total.
Paul McNicoll and Andy Crichton completed a 55-mile walk from Hearts' Tynecastle Stadium in Edinburgh to Tannadice in Dundee.
