Adaptive Control Constrains (ACC) as applied to machine tool systems refers to the regulation of the cutting process characteristics such as spindle power, cutting force etc., by varying the only changeable process parameters which are feedrate and cutting speed. Even a simple ACC system, as in this case, in which the cutting force is regulated by changing the feedrate, is quite complex. Experiments with this simple system, implemented on a computerized numerical control (CNC) lathe, have shown that the CNC/ACC system can become unstable due to changes in depth-of-cut or spindle speed. This paper presents stability analysis of the above CNC/ACC system, thus making it possible to select appropriate gains which will maintain the system stable. Also, experimental results, which describe the stability region of such a system, will be provided.