Passive safety systems are an important feature of currently designed and constructed nuclear power plants. They operate independent of external power supply and manual interventions and are solely driven by thermal gradients and gravitational force. This brings up new needs for performance and reliably assessment. This paper provides a review on fundamental approaches to model and analyze the performance of passive heat removal systems exemplified for the passive heat removal chain of the KERENA boiling water reactor concept developed by Framatome. We discuss modeling concepts for one-dimensional system codes such as ATHLET, RELAP and TRACE and furthermore for computational fluid dynamics codes. Part I dealt with numerical and experimental methods for modeling of condensation inside the emergency condenser and on the containment cooling condenser. This second part deals with boiling and two-phase flow instabilities.