The matter was deferred till Friday as both the pleas were listed before different benches of the high court.
Both lawmakers Anil Bajpai and Col. Devinder Sehrawat had moved the high court, challenging a recent order by a single bench of this court which refused to grant any relief to the politic.
On July 8, a single judge bench presided over by Justice Vibhu Bakhru turned down the pleas saying they were devoid of merit and not informative in procedure.
Petitioner Sehrawat too had addressed in person before the court.
However, in a partial relief, the court has granted two days' time to the AAP rebels to submit their replies before the speaker.
The petition also sought direction to the speaker to constitute an appropriate committee to adjudicate the anti-defection proceedings initiated against him by the AAP.
In his plea, Bajpai alleged that Speaker Ram Niwas Goel is a politically active member of the AAP and hence, his interests lie within the party as a result of which the proceedings would be biased.
On July 12, the AAP said "two of its rebel MLAs", who reportedly joined the Bharatiya Janata Party (BJP) ahead of the Lok Sabha polls, have told the Delhi Assembly Speaker that they were with the AAP and did not join the BJP.
The chief spokesperson of AAP, Saurabh Bharadwaj, said that on May 3 and 6, the senior leadership of the BJP, including Shyam Jaju, Vijay Goel and Vijendra Gupta, had claimed that two AAP MLAs Anil Bajpai and Colonel Devinder Sehrawat had left the AAP and joined the BJP.
( With inputs from IANS )