Here, negative normal stress differences are reported in capillary suspensions, i.e. particle suspensions in a two-fluid system that creates strong capillary attractions, at a solid concentration of 25%, and a volume fraction that has heretofore been considered too low to show such normal stress differences. Such capillary suspensions have strong particle networks and are shear thinning for the entire range of shear rates studied. Capillary suspensions exist in two states: a pendular state when the secondary fluid preferentially wets the particles, and a capillary state when the bulk fluid is preferentially wetting. In the pendular state, the system undergoes a transition from a positive normal stress difference at high shear rates to a negative stress difference at low shear rates. These results are an indication of flexible flocs in the pendular state that are able to rotate to reorientate in the vorticity direction under shear. Analogous experiments were also conducted for the capillary state, where only a negative normal stress difference occurs. The capillary state system forms more network contacts due to droplet breakup at higher shear rates, which enhances the importance of hydrodynamic interactions in the non-colloidal suspension.