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During the deformation of polycrystals, pronounced strain gradients may occur at grain boundaries between grains whose misorientations lead to a large mismatch in their deformation behaviour. Hence, even under globally uniaxial and homogeneous strains, internal stresses will arise that must be characterized by nonlocal plasticity models. In this work, such a nonlocal constitutive model is formulated based on the concept of densities of geometrically necessary superdislocations in an isotropic elastic-plastic medium. Since the deformation of individual grains is considered, crystal plasticity models are applied that take into account plastic slip on crystallographic planes. This new nonlocal constitutive model is applied to describe the deformation of a polycrystal under the influence of plastic strain gradients caused by isotropic and kinematic strain hardening. It is found that isotropic hardening originating from plastic strain gradients amplifies deformation heterogeneities stemming from different Schmid factors in neighbouring grains. However, the kinematic hardening resulting from plastic strain gradients tends to reduce such deformation heterogeneity. Thus, the capability of a polycrystal to deform uniformly is determined by the competition between isotropic and kinematic hardening. Finally, the model is applied to explain why grain refinement is an efficient way to improve material strength and ductility at the same time.