Abstract Correlations between optical flashes and gamma-ray emissions in gamma-ray bursts (GRBs) have been searched in order to clarify the question of whether these emissions occur at internal and/or external shocks. Among the most powerful GRBs ever recorded are GRB 080319B and GRB 130427A, which at early phases presented bright optical flashes possibly correlated with γ-ray components. Additionally, both bursts were fortuitously located within the field of view of the TeV γ-ray Milagro and HAWC observatories, and although no statistically significant excess of counts were collected, upper limits were placed on the GeV–TeV emission. Considering the synchrotron self-Compton emission from internal shocks and requiring the GeV–TeV upper limits, we found that the optical flashes and the γ-ray components are produced by different electron populations. Analyzing the optical flashes together with the multiwavelength afterglow observation, we found that these flashes can be interpreted in the framework of the synchrotron reverse shock model when outflows have arbitrary magnetizations.