The static bifurcation of the two-phase natural circulation (TPNC)system was studiedtheoretically and numerically. By the DERPAR algorithm the solutiondiagram was calculated, which shows that the static bifurcationoccurs undersome conditions in the TPNC systems. Also, it shows that, in a region of multiplesolutions, the static instability may occur. It is defined as a region ofthermal-siphon instability induced flow rate jumping. By means of thesolution diagram, the stability margin can be determined in this region.Furthermore, the heat input at the peak of the solution diagram is defined as themaximum capacity of heating load that can be used to judge the capacityof the TPNC ofa given geometry topological structure. Meanwhile, it is interestingthat the TPNCsystemshave the hysteresis phenomenon defined as thermal-siphon hysteresis.Some parametriceffects related were also studied.