Hearts and Partick Thistle say it is “unbelievable” that the Scottish FA accused them of taking legal action to reverse their demotion.
The court referred their case against the SPFL to arbitration, which is due to take place in the coming days.
The SFA says that, first of all, not using arbitration, the clubs violated their rules.
Hearts sent from the Premier League and Thistle from the Championship requested that SFA proceedings be postponed.
The governing body set a date on August 6 for the disciplinary case.
“We are incredulous that we received a notification from the SFA about the circumstances,” – Joint statement said.
“It is cruel of them to demand representation from both clubs by July 20, when, in accordance with their own charters, we are actively participating in arbitration.
“Since we should focus on this, we have already asked the SFA to review the deadlines so that we are properly prepared and represented. This is the smallest thing we should expect from the process. ”
Harts and Thistle first went to the Sessional Court after their rejection was not prevented by the SPFL's failed league proposal. The offer would also give Stranraer a reprieve from relegating the First League.
At the first hearing, Lord Clark decided that the rules of the football authorities meant that the case should be tried by an independent tribunal established in accordance with the rules of the SFA.
If successful, both clubs will be reinstated in their original divisions, and promotions for Dundee United, Raith Rovers and Cove Rangers will be banned.