The static bifurcation of the two-phase natural circulation (TPNC) system was studied theoretically and numerically. By the DERPAR algorithm the solution diagram was calculated, which shows that the static bifurcation occurs under some conditions in the TPNC systems Also, it shows that, in a region of multiple solutions, the static instability may occur. It is defined as a region of thermal-siphon instability induced flow rate jumping. By means of the solution diagram, the stability margin can be determined in this region. Furthermore, the heat input at the peak of the solution diagram is defined as the maximum capacity of heating load that can be used to judge the capacity of the TPNC of a given geometry topological structure. Meanwhile, it is interesting that the TPNC systems have the hysteresis phenomenon defined as thermal-siphon hysteresis. Some parametric effects related were also studied.