Gap-graded cohesionless soils, comprising mixtures of fine and coarse grains, pose a particular challenge in soil mechanics. Reasoning and experimental data indicate that some of the finer grains may exist in the void space without transmitting any stress. A number of authors have proposed considering at least some of the volume of these particles along with the void space when calculating the void ratio in the case of low fines contents. The concept of a transitional fines content has been proposed, i.e., a fines content delineating materials whose behavior is dominated by the coarser grains and materials whose behavior is determined by the finer grains. This contribution uses discrete element method (DEM) simulations to explore the nature of stress transmission in gap-graded materials comprised of spherical particles. Partitioning the stress tensor by considering the contributions of the contacts between coarse particles, the contacts between coarse and fine particles, and the contacts between fine particles is shown to provide useful insight into the contribution of each type of particle to the overall stress transmission. In general, for the mixtures considered here, the coarse-coarse contacts transmit a greater range of forces and a greater average force. For the mixture with size ratio of 3.7, the range of contact force magnitudes transmitted by each contact type reduces with increasing fines content and increasing sample density. This sensitivity is more evident for the lower fines contents studied.