In numerical simulations of particulate systems, the shape of particles plays an important role in capturing the overall mechanical behavior. It influences the motion of each particle and how particles interact with each other. More realistic particle geometries improve the model fidelity, but they also require more computing effort for solving contact, which consists in their basic mechanism of interaction. In this context, the work presents a complete contact detection algorithm to be used with particles whose boundaries are described by non-uniform rational B-splines (NURBS), which allows us to create shapes as generic as needed [1]. Such algorithm encompasses a hierarchy of both global and local searches for contact. The formulation of the local contact problem is based on a master-to-master approach, as shown in [2,3]. It verifies the contact status and quantifies the maximum penetration between particles in case of contact, which is the basic quantity to evaluate contact forces. The formulation employs computer graphics concepts – Minkowski sum, configuration space obstacle (CSO) and support mapping – to obtain the maximum penetration between particles through minimization schemes. The focus is on smooth convex NURBS particles. When dealing with closed geometries, one may use only one or multiple NURBS parameterizations (patches) properly arranged in space to create the desired particle shape. It is shown that both strategies have singularities and/or geometric imperfections that make it difficult to treat contact in such regions. Choosing multiple NURBS to model particles, the main novelty of this work is the adaptation of the degeneration technique proposed in [4] to deal with contact at the connections between patches, which are regions susceptible to the occurrence of geometric imperfections. Besides presenting the formulation, the work shows examples that demonstrate the behavior of the proposed contact algorithm for NURBS particles.