This paper addresses the problem of contact force control for multiple contacts distributed over multiple links in a robot. This is of importance when performing complex tasks in unstructured environment, particularly in humanoid robot applications. The proposed multicontact control framework provides a new way of defining the operational space coordinates, which facilitates the specification of multiple contact control. The contact force space on multiple links is constructed as an operational space for the highest priority task. Motion control, given lower priority, can be executed using the rest of degree of freedom within the null-space of the force control. The dynamic control structure, then, provides a means to control each contact force and motion independently. This dynamic decoupling enables each contact force controller to utilize linear control theories. In particular, the contact force controllers adopt full state feedback control and estimation methods to produce robust performance with respect to modeling and parameter uncertainties. The effectiveness of the multiple contact control framework was demonstrated using a PUMA560 manipulator, with multiple contacts on the end-effector and third link. The demonstrated tasks involved controlling each of the contact forces with null-space motion.