Three kinds of definitions of disentanglement of 3-particle systems are given. Three basic regulations of a 3-particle system pure-state disentanglement are completely analyzed. It is shown that there are some sets of 3-particle entangled states that can be disentangled into product states or 1-particle product and 2-particle separable states or fully separable states, but a universal disentangling machine into product states or 1-particle product and 2-particle separable states or fully separable states cannot exist.