Conventionally, the stability of xenon oscillations is estimated by solution of the time-dependent neutron diffusion equation, coupled with iodine and xenon equations, by finding out the damping ratios in each case. This is performed for different initial perturbations and core burnup conditions and is a very time-consuming and tedious process. Some earlier studies include linear stability estimation, which is valid for small perturbations, but not much work has been done in nonlinear stability analysis for spatial xenon oscillations in particular. In this paper, an approach for carrying out bifurcation analysis of xenon oscillations in large pressurized heavy water reactors (PHWRs) is demonstrated using reduced-order models. The reduced-order model for studying spatial xenon oscillations consists of multipoint kinetic equations coupled with xenon and iodine equations along with explicit fuel and coolant temperature feedback. Both subcritical Hopf bifurcation and supercritical Hopf bifurcation in different parameter planes exist, which leads to unstable limit cycles in the linearly stable region (subcritical Hopf bifurcation) and stable limit cycles in the linearly unstable region (supercritical Hopf bifurcation). The stability map provides a total picture of the stability of the out-of-phase oscillations in a PHWR. Depending on the value of the fuel temperature coefficient of reactivity and coolant temperature coefficient of reactivity, one can determine the operating power level above which the out-of-phase xenon oscillations start to grow. This model can be used to analyze nonlinear stability characteristics without spatial power control, which is helpful in identification of stable/unstable regimes in different parameter spaces and is likely to aid in reactor design.