A Solid Oxide Fuel Cell-Hybrid System is mainly composed of three parts: the stack, the anodic recirculation system with fuel feeding, and the cathodic side (air side) where turbomachinery and heat exchangers are installed. In Part A of this work the transient models of the fuel cell are described, while in Part B the anodic side is investigated. Many previous studies have been carried out on the cathodic side at the Thermochemical Power Group facility to simulate the transient behavior of the main components such as compressors, expanders and heat exchangers. In this paper attention is focused on the integration of the transient models of the hybrid system components. Following the on and off-design analysis of the SOFC-HS the transient response of the system from an electrochemical, fluid dynamic and thermal point of view has been studied at several operating conditions.