We investigate the stability of gas bubbles formed at saturated (bubble-point) conditions during two-component ( CO2 , H2O), two-phase (gas, liquid) flow by developing and analyzing a 2×2 dynamical system describing flow through a single pore to study the dynamics of gas bubble formation and evolution. Our analysis indicates that three regimes occur at conditions pertinent to petroleum reservoirs. These regimes correspond to a critical point changing type from an unstable node to an unstable spiral and then to a stable spiral as flow rates increase. In the stable spiral case, gas bubbles will achieve a steady-state finite size only if they form within the attractor region of the stable spiral. Otherwise, all gas bubbles that form undergo, possibly oscillatory, growth and then dissolve completely. Under steady flow conditions, this formation and dissolution repeats cyclically.