In the last years, an increasing interest in multistable structures has been observed. Multistable systems are generally attained by a chain of bistable units connected by rigid or flexible elements. However, little is known about their nonlinear static and dynamic responses. In this work, a detailed nonlinear static and dynamic analysis of multistable systems formed by two shallow bistable units is conducted, specifically, two von Mises trusses or two arches, connected in both cases by rigid or flexible elements. For this, the nonlinear equilibrium equations and equations of motion are obtained through the principle of stationary potential energy and Hamilton s principle, respectively, considering a linear elastic material. Using continuation algorithms, the nonlinear equilibrium paths are obtained, and stability analyzed using the principle of minimum potential energy. Multiple equilibrium paths are identified, leading to several stable and unstable coexisting solutions and potential wells with are closely linked to the systems symmetries. The effect of unavoidable initial imperfections is also clarified. The nonlinear dynamics and bifurcations of systems under harmonic forcing are studied using bifurcation diagrams, Poincaré maps and cross-sections of the basins of attraction. The effect of a static pre-load on global dynamics is also studied. Due to the bifurcation sequences emerging from each stable equilibrium configuration, a high number of coexisting solutions are observed, both periodic and aperiodic, leading to complex basins of attraction with broadening fractal regions. On the one hand, these scenarios can be valuable in several applications. On the other hand, multiple attractors and their fractal basins can lead to the loss of stability and dynamic integrity. Therefore, knowledge on the nonlinear static and dynamic behavior of multistable systems is primordial in any engineering application. As an application example, a system composed by two von Mises trusses is used in the process of energy harvesting through piezoelectric elements. The highly nonlinear behavior results in large amplitude oscillations for a wide range of excitation frequency, increasing its efficiency and applicability.