In this article, we present several examples of special nonlinear conjugate gradient directions for nonlinear (non-convex) multi-objective optimization. These directions provide a descent direction for the objectives, independent of the line-search. This way, we can provide an algorithm with simple, Armijo-like backtracking and prove convergence to first-order critical points. In contrast to other popular conjugate gradient methods, no Wolfe conditions for the step-sizes have to be satisfied. Besides investigating the theoretical properties of the algorithm, we also provide numerical examples to illustrate its efficacy.