The existence of slow and monotone solutions with respect to a continuous pre-order is proved for differential inclusions defined on a closed convex subset of R4. First we examine the ‘projected system’, and prove that it is equivalent to a differential variational inequality. We then establish the existence of monotone trajectories. Subsequently, we prove the existence of slow monotone solutions for a class of differential inclusions, satisfying a Nagumo-type condition. Finally we prove a convergence result.