The Hight Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory monitors the gamma-ray sky in the energy range from 100 GeV to 100 TeV and has detected two very high energy (VHE) blazars: Markarian 421 (Mrk 421) and Markarian 501 (Mrk 501) in 1.5 years of observations. In this work, we present the spectral analysis above 1 TeV of both sources using a maximum likelihood method and an artificial neural network as an energy estimator. The main objectives are to constrain the spectral curvature of Mrk 421 and Mrk 501 at ∼5 TeV using the EBL models from Gilmore et al. (2012) and Franceschini et al. (2008).