The VHE component from at least two GRBs, i.e., GRB180720B and GRB190114C, has been detected in the afterglow phase. We systematically analyzed 199 GRBs detected by Fermi-LAT during 2008-2019. If an additional high-energy component exists in the afterglows of Fermi-LAT GRBs, the best-fit spectral model could be a broken power-law (BPL) model with an upturn above a break energy. We compare the afterglow spectra using PL and BPL representations. Out of the 30 GRBs with >10GeV photons that arrived after T90, 25 GRBs are tentatively or significantly detected at 0.1-200 GeV after 2*T90. The spectrum of GRB131231A shows an upturn above a break of 1.6+-0.8~GeV, supporting the BPL model. For GRB131231A, we performed a modeling of its X-ray and gamma-ray spectra, and found that the SSC model can explain the upturn with acceptable parameter values. In the cases of GRBs 190114C, 171210A, 150902A, 130907A, 130427A, and 090902B, the improvement of the BPL fit compared to the PL fit is tentative or marginal. There is no conclusive evidence that an additional higher energy component commonly exists in Fermi-LAT GRB afterglows, except for a group of Fermi-LAT GRBs mentioned above. Such an additional high-energy component may be explained by the synchrotron self-Compton mechanism. Current and future VHE observations will provide important constraints on the issue.
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