The Tribunal's decision follows appeals filed by the two airlines against the Competition Commission of India (CCI) order passed in November 2015.
Penalties of Rs 63.74 crore and Rs 42.48 crore were imposed on InterGlobe Aviation and SpiceJet, respectively.
InterGlobe runs budget carrier IndiGo. Staying the CCI order, the tribunal said it would hear the matter next in March.
Besides InterGlobe and SpiceJet, CCI had also penalized Jet Airways for concerted action in fixing and revising Fuel Surcharge (FSC) for transporting cargo.
The three carriers were also directed to cease and desist from indulging in anti-competitive practices.
CCI's order followed a complaint filed by Express Industry Council of India, which had alleged that the five airlines indulged in anti-competitive practices.
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