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We theoretically demonstrate the novel multibistability and multistability features of two coupled active microrings. The continuation method is utilized to solve the parametric nonlinear equations of these two-active-microring systems, and the bifurcation theory is used to investigate the special points, which exist in continuation process. The novel results, which are interpreted by the nonlinear transmission spectrum, arise from gain saturation and the optical field coupling between these two nonlinear rings. Besides the common multibistability, which consists of serial S-shaped hysterical loops, the multibistability, which takes on novel shapes, such as the hat-shaped, knife-shaped, S-shaped butterfly, and inverted double-S-shaped is also demonstrated. The novel multistability includes inverted double-S-shaped tristability, woodpecker-shaped tristability, duke-shaped tristability, grasshopper-shaped tristability, and pseudo-quadristability. The electrical and optical control processes of the stability about these two coupled active microrings are also investigated. Results show that the on-off jumping threshold of this stability can be adjusted via changing the power of the light, which inputs from the add-drop port, and the type of this stability can also be changed by altering the injected current on each active microring.