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Rapid federated bilevel optimization (FBO) developments have attracted much attention in various emerging machine learning and communication applications. Existing work on FBO often assumes that clients participate in the learning process with some particular pattern (such as balanced participation), and/or in a synchronous manner, and/or with homogeneous local iteration numbers, which might be hard to hold in practice. This paper proposes a novel Anarchic Federated Bilevel Optimization (AFBO) algorithm, which allows clients to 1) participate in any inner or outer rounds; 2) participate asynchronously; and 3) participate with any number of local iterations. The AFBO algorithm enables clients to participate in FBO training flexibly. We provide a theoretical analysis of the learning loss of AFBO for both cases of non-convex and strongly convex loss functions. The convergence results of the AFBO algorithm match that of the existing benchmarks. Numerical studies are conducted to verify the effectiveness of AFBO.