Evidence is presented for the electroweak (EW) production of two jets (jj) in association with two Z-bosons and constraints on anomalous quartic gauge couplings are set. The analysis is based on a data sample of proton-proton collisions at root s = 13 TeVcollected with the CMS detector in 2016-2018, and corresponding to an integrated luminosity of 137 fb(-1). The search is performed in the fully leptonic final state ZZ -> lll'l', where l, l' = e, mu. The EW production of two jets in association with two Zbosons is measured with an observed (expected) significance of 4.0 (3.5) standard deviations. The cross sections for the EW production are measured in three fiducial volumes and the result is sigma(EW)(pp -> ZZjj -> lll'l'jj) = 0.33(-0.10)(+0.11)(stat)(-0.03)(+0.04)(syst) fbin the most inclusive volume, in agreement with the standard model prediction of 0.275 +/- 0.021fb. Measurements of total cross sections for jj production in association with two Zbosons are also reported. Limits on anomalous quartic gauge couplings are derived in terms of the effective field theory operators T0, T1, T2, T8, and T9. (C) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license.