The case is scheduled to be heard at the North West High Court in Mahikeng on Friday, on the eve of the beginning of the ANC's national conference in Mangaung.
A lack of response from the ANC and the fact that the party was not represented in court were the main reasons the matter could not be heard urgently on Tuesday.
The Mail & Guardian has seen a letter addressed to provincial secretary Kabelo Mataboge from Semaushu Attorneys, a Mahikeng-based law firm, that said the lawyers represent unhappy ANC branches.
In the letter, the lawyers said the province's process leading to next week's national conference was "flawed and therefore renders the entire process unlawful".
"We are therefore instructed to inform your good office not [to] continue with further processes, as branches intent [sic] challenging validity of the said process," the letter said.
The lawyers also requested Mataboge to guarantee in writing that the ANC would not proceed with further processes for Mangaung preparation, but that did not happen.
Dali Mpofu, who represented another disgruntled ANC group in the Free State is the senior counsel for the North West faction.
ANC chairperson Supra Mahumapelo claimed the majority of provincial executive committee (PEC) members did not know about the letter. There was a last minute scramble on Tuesday afternoon by PEC members for an emergency meeting to plan a way forward.
The North West is divided between a group supporting ANC president Jacob Zuma for re-election led by Mahumapelo and another group campaigning for deputy president Kgalema Motlanthe to replace Zuma led by Mataboge.
Xolile Mqume, a leader of the concerned branch members, said they want the court to interdict North West delegates from attending the Mangaung conference.
"It doesn't matter even if we don't contribute. It won't be the first time that the North West is not seen as the major player in the ANC," Mqume said.
He added that the court application is supported by around 700 branch members from all four regions of the province.
Despite some ANC members were unhappy with the province's nomination conference that took place two weeks ago, ANC secretary general Gwede Mantashe gave it a thumbs up.
Said an ANC pro-change member in the North West, who agrees with the court application: "We'd rather not go there [Mangaung] instead of sending people whose agenda we don't know or understand."
North West delegates are scheduled to travel to the conference on Saturday.