This paper considers the effect of an antistall tool on the dynamics of deep drilling systems. Field results show that the antistall tool increased the rate of penetration (ROP) of drilling systems when compared with ROP in offset wells drilled without this tool. We developed a model-based approach to investigate the effect of this downhole tool on the ROP and on the mechanical specific energy. Toward this, a drillstring model including the antistall tool was constructed; it describes the coupled axial/torsional dynamics in the form of delay differential equations. Simulation results and a dynamic analysis based on averaging the obtained steady-state response show that an increased drilling efficiency was obtained using the antistall tool, resulting in a higher ROP.