Hearts head coach Robbie Neilson and Inverness manager John Hughes have been issued with notices of complaint by the Scottish FA's compliance officer.
Both are alleged to have breached SFA rules by criticising officials in interviews after Inverness drew with Dundee and Hearts lost to Hamilton.
Principal hearings have been set for 1 October and both men have until 22 September to respond.
The Hearts head coach also claimed he was expecting one of his players to be dismissed when he found out who the officials were. Neilson was later asked by the SFA to explain his comments.
"The game has been ruined by a decision that is not a sending-off," said Neilson on 29 August.
"We actually practised going down to 10 men because of the environment we're coming to and the officials who are taking the game and we have to do that.
"In the recent past, the statistics involving the officials have shown a lot of red cards against us, so we have to prepare for it.
"The next time we get these officials, we will again train with 10 men."
Hughes, meanwhile, was unhappy with decisions made by Andrew Dallas during the 1-1 draw at Dens Park.
The Caley Thistle manager said Dallas brought an "edginess and a nervousness" to the game and was not "ready to referee top-flight football".