The Large Hadron Electron Collider and the Future Circular Collider-hadron electron with high centerof-mass energy and luminosity allow to better understand the Standard Model and to examine new physics beyond the Standard Model in the electroweak sector. Multi-boson processes permit for a measurement of the gauge boson self-interactions of the Standard Model that can be used to determine the anomalous gauge boson couplings. For this purpose, we present a study of the process ep -> nu(e)gamma gamma j at the Large Hadron Electron Collider with center-of-mass energies of 1.30, 1.98 TeV and at the Future Circular Collider-hadron electron with center-of-mass energies of 7.07, 10 TeV to interpret the anomalous quartic WW gamma gamma gauge couplings using a model independent way in the framework of effective field theory. We obtain the sensitivity limits at 95% Confidence Level on 13 different anomalous couplings arising from dimension-8 operators. The best limit in f(Mi)/Lambda(4)(i= 0, 1, 2, 3, 4, 5, 7) parameters is obtained for fM(2)/Lambda(4)parameter while the best sensitivity derived on fTi/Lambda(4)(i= 0, 1, 2, 5, 6, 7) parameters is obtained for f(T5)/Lambda(4). In addition, this study is the first report on the anomalous quartic couplings determined by effective Lagrangians at epcolliders. (C) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).