SSC emission from a reverse shock has been suggested as the origin for the high energy component lasting 2 s in the prompt phase of GRB98080923 (Fraija et al. 2012). The model describes spectral indices, fluxes and the duration of the high-energy component as well as a long keV tail present in the prompt phase of GRB980923. Here, we present an extension of this model to describe the high-energy emission of GRB090926A. We argue that the emission consist of two components, one with a duration less than 1s during the prompt phase, and a second, longer-lasting GeV phase lasting hundred of seconds after the prompt phase. The short high-energy phase can be described as SSC emission from a reverse shock similar to that observed in GRB980923, while the longer component arises from the forward shock. The main assumption is that the jet is magnetized and evolves in the thick-shell case, and the calculated fluxes and break energies are all consistent with the observed values. A comparison between the resulting parameters obtained for GRB980923 and GRB090926A suggests differences in burst tails that could be attributable to the circumburst medium, and this could account for previous analyses reported in the literature for other bursts. We find that the density of the surrounding medium inferred from the observed values associated to the forward shock agrees with standard values for host galaxies such as the one associated to GRB090926A.