The present work represents a little but valuable contribution to the advancement of the research in the field of the neutron kinetics of innovative nuclear reactors. As modern computer frames are becoming more and more performing and because the treatment of innovative nuclear reactor systems requires high accuracy results, the neutron transport theory is currently being adopted for full-core calculations. Embracing such tendency, in the present work the quasi-static approach has been adopted and implemented for the design of computational codes capable of performing reliable transient calculations. The underlying idea has been the development of the kinetic module on top of the transport solver, in such a way that the former can be flexibly plugged into the codes ystem, independently from the transport solver itself. In particular, two computer codes have been developed: the first has been designed coupling the stand-alone DRAGON transport solver to an "ad hoc" reactor kinetic module; the second code has been developed within the ERANOS code system. A Java object-oriented platform developed by CEA-Cadarache constitutes the framework where a kinetic package has been designed, adopting the code's API (Application Programming Interface) for the full integration in the code system. The well known Improved Quasi-static Method (IQM) and the innovative Predictor-Corrector Quasi-static Method (PCQM) have been implemented in both computer codes. In the present work a deep analysis of the two types of quasi-static schemes has been carried out as well as the description and validation of the aforementioned computer codes.