The effect of electron-phonon interaction on the transport properties of two-dimensional electron gas in a strong transverse magnetic field is investigated. Corrections to nondiagonal (Hall) components of electrical and heat conductivities and thermopower tensors are obtained in the context of the diagrammatic technique and are shown to be essential in a wide range of temperatures and magnetic fields. Experimental conditions for the observation of electron-phonon interaction effects in the electronic transport in the quantum-Hall-effect regime are discussed.