Hlophe's lawyer Barnabas Xulu said the JSC would be replying to supplementary papers the Hlophe team filed last week at the invitation of Judge Nigel Willis, who is handling Hlophe's action in the High Court in Johannesburg.
Hlophe applied to that court for an urgent interdict to declare the commission's hearings void because he believed they were biased.
On reserving judgment, Willis advised the two sides to try to reach a settlement before he hands down judgment.
The judges of the Constitutional Court lodged a complaint with the JSC last year that Hlophe had allegedly approached two judges inappropriately over a judgment relating to President Jacob Zuma.
Hlophe in turn complained to the JSC about the judges' decision to make the matter public before he had a chance to answer to the accusation.
The hearings began without Hlophe on April 1 because he was sick, and continued after his sick note had expired after the JSC refused an application to postpone.
A video of a boy being forced by his parents to run almost naked in the snow has sparked an uproar.
Cosatu met with the Public Protector to discuss its numerous complaints against Premier Helen Zille.
Marine ruins have been discovered by builders working at the V&A Waterfront in Cape Town.
