This article focuses on issues related to control and operability of a Solid Oxide Fuel Cell (SOFC) - Gas Turbine (GT) hybrid system with single-shaft GT configuration. The models of all the components of the hybrid system are developed and integrated to constitute the hybrid system. An autonomous power grid is modeled as load. The main control objectives considered are control of Fuel Utilization (FU) in the SOFC and SOFC solid temperature during dynamic operation of the hybrid system.