The following basic question is studied here: In the relatively stable molecular environment of a vertebrate body, can a dynamic idiotypic immune network develop a natural tolerance to endogenous components? The approach is based on stability analyses and computer simulation using a model that takes into account the dynamics of two agents of the immune system, namely B-lymphocytes and antibodies. The study investigates the behaviour of simple immune networks in interaction with an antigen whose concentration is held constant as a function of the symmetry properties of the connectivity matrix of the network. Current idiotypic network models typically become unstable in the presence of this type of antigen. It is shown that idiotypic networks of a particular connectivity show tolerance towards auto-antigen without the need forad hocmechanisms that prevent an immune response. These tolerant network structures are characterized by aperiodic behaviour in the absence of auto-antigen. When coupled to an auto-antigen, the chaotic attractor degenerates into one of several periodic ones, and at least one of them is stable. The connectivity structure needed for this behavior allows the system to adopt particular dynamic concentration patterns which do not lead to an unbounded immune response. Possible implications for the understanding of autoimmune disease and its treatment are discussed.