Externally bonded (EB) fiber reinforced polymers (FRP) composites represent an efficient and alternative solution for the retrofitting of existing structures. Carbon fibers reinforced polymers (CFRP) composites have been used for the strengthening of existing metallic structures to improve their load bearing capacity and fatigue life. Existing studies have revealed that debonding of the CFRP from the steel substrate is one of the main failure modes in these applications and therefore the interfacial behavior plays a crucial role in the system response. Two main classes of epoxy adhesives are usually adopted and referred to in literature as brittle and ductile adhesives. In this paper, a numerical characterization of the system response is provided with the adoption of an exponential cyclic cohesive zone law (CCZL) embedded into a finite element (FE) framework. Specimens bonded with both brittle-linear or ductile-nonlinear epoxy adhesives are investigated, when subjected to both monotonic and cyclic loading conditions and their differences highlighted. A parametric analysis is performed to investigate the effects of the key design parameters on the system response in different loading conditions and with different epoxy adhesives.