Source separation and signal distortion are theoretically analyzed for the FF-BSS systems implemented in both the time and frequency domains and the FB-BSS system. The FF-BSS systems have some degree of freedom, and cause some signal distortion. The FB-BSS has a unique solution for complete separation and distortion free. Next, the condition for complete separation and distortion free is derived for the FF-BSS systems. This condition is applied to the learning algorithms. Computer simulations by using speech signals and stationary colored signals are carried out for the conventional methods and the new learning algorithms employing the proposed distortion free constraint. The proposed method can drastically suppress signal distortion, while maintaining high separation performance. The FB-BSS system also demonstrates good performances. The FF-BSS systems and the FB-BSS system are compared based on the transmission time difference in the mixing process. Location of the signal sources and the sensors are rather limited in the FB-BSS system.