The ANC argued the party should deal with political problems in a political forum, rather than running to court.
ANC legal counsel Phazha Ngandwe said the matter was brought to the court prematurely.
The EFF's argument is that both Mokgalapa and Mathebe simply aren't trusted by the majority in the council.
The party's asking why they should be reinstated at all.
The DA's argument remains the same: That the resolutions of the special council meeting should be nullified because proper processes weren't followed.
Judgment has been reserved. Whichever way the judgment goes, the ANC and EFF say they will support each other to make sure the DA loses the capital city.
Tshwane residents will know in about a week if they'll have a new mayor come the new year.