Joints of multibody systems can keep their constraints under the condition of very small clearances. However, the frictions in a joint are involved in the constraint forces, as the result of the correlations between the state of the systems and form of contact in the joint. Based on the equivalence of points contact and distributed contact, we presented the formulations of frictions in typical joints with small clearances on the assumption that the deformations of joints are negligible. An example was given to validate the presented formulations.