Artificial multi-joint musculoskeletal systems consisting of serially connected links driven by monoarticular and multiarticular muscles, which are often inspired by vertebrates, enable robots to elicit dynamic, elegant, and flexible movements. However, serial links driven by multiarticular muscles can cause unstable motion (e.g., buckling). The stability of musculoskeletal mechanisms driven by antagonistic multi-joint muscles depends on the muscle configuration, origin/insertion of muscles, spring constants of muscles, contracting force of muscles, and other factors. We analyze the stability of a multi-serial-link mechanism driven by antagonistic multi-joint muscles aiming to prevent buckling and other undesired motions. First, we theoretically derive the potential energy of the system and the stable condition at the target point. Then, we validate the method through dynamic simulations and experiments. We confirm that we can construct a stable multiarticulate musculoskeletal system using the proposed formulation and conditions.