The dynamical evolution process of the coupled system connecting two nonlinear electrical circuits with suitable circuit is investigated. The bifurcation behavior as well as the ways to chaos of the two subsystems is presented. It is pointed out when both of the two subsystems behave as periodic, the coupled system may also be led to chaos via cascading of period-doubling bifurcations. Meanwhile, in the chaotic region, critical increase of period as well as period-adding bifurcation can be observed. As to the interaction between periodic movement and the chaotic oscillation, the original periodic subsystem may chaotically oscillate around the original orbit. The amplitude associated with the oscillation increases rapidly, resulting in the obvious chaotic characteristics. On the contrary, the periodic subsystem may not only cause the instability of the chaotic subsystem, but also lead to change of the chaotic structures.