<p>This paper develops a Newton’s descent method with nonmonotone line search strategies for solving robust counterparts, i.e., robust multiobjective problems, of uncertain multiobjective optimization problems (UMOP) under finite uncertainty. The uncertainty in the objective functions is addressed through an objective-wise maximum-type robust reformulation, which converts the original uncertain problem into a deterministic robust model. At each iteration, a Newton’s descent direction is obtained by solving an auxiliary subproblem, and a nonmonotone line search technique is employed to determine the step length, thereby allowing flexibility in the acceptance of trial points and improving convergence behavior. Two variants of nonmonotonicity, namely maximum-type and average-type, are proposed, and the corresponding algorithms are formulated. Global convergence as well as quadratic convergence rate of the proposed methods are established under standard assumptions. Finally, extensive numerical experiments are conducted to demonstrate the effectiveness of the proposed algorithms, and their performance is compared with the existing Newton’s descent method based on a monotone Armijo-type inexact line search using performance profiles.</p>