Two-phase flow in parallel heated channels is prone to symmetry breakdown resulting in mass flow maldistribution. Moreover, in the presence of compressible volume, such systems also undergo pressure drop oscillations (PDO). The performances of such systems depend on the effect of these flow instabilities. However, the simultaneous occurrence of these two- phenomena has been rarely reported in the literature. In the present work, an approach is applied in a two channels system to demarcate the parameter space of mass flow rate and inlet temperature into several areas, where these two phenomena take place. The loss in the symmetry in the flow rate is observed as the mass flow rate is varied, which leads to flow maldistribution. The PDO are also observed for specific values of mass flow rate in the system. One unique feature of the parallel channel system is the existence of the oscillatory and stable (albeit asymmetric) states at the same parameter values. For these parameter values, the final state of the system is dependent on the type of initial disturbance. The flow maldistribution due to symmetry breakdown is identified by the pitchfork bifurcation, and oscillations of mass flow rate are identified by the presence of Hopf bifurcation. Moreover, the physical interpretation of the different phenomena in the system is carried out using internal and external pressure drop characteristics curves.