A criterion for linearized stability with respect to both the pressure- drop and the density-wave oscillations is developed for a single channel upflow boiling system operating between constant pressures with upstream compressibility introduced through a surge tank. Two different two-phase flow models, namely a constant-property homogeneous flow model and a variable property drift-flux model, have been employed. The conservation equations for both models and the equations of surge tank dynamics are first linearized for small perturbations and the stability of the resulting set of equations for each model are examined by use of Nyquist plots. As a measure of the relative instability of the system, the amounts of the inlet throttling necessary to stabilize the system at particular operating points have been calculated. The results are compared with experimental findings. Comparisons show that the drift-flux formulation offers a simple and reliable way of determining the instability thresholds. The homogeneous flow model is good to acquire a physical understanding of the problem.