In order to obtain radicals of a Г-ring determined by strong nilpotency, nilpotency, and strongly nil property, we introduce a general method. Let P be an arbitrary property of Γ-rings. For any Γ-ring we construct a quasi-P radical determined by P. If P is homomorphically closed, then this quasi-P radical can be constructed by transfinite induction. We next study the relations of radicals among the quasi-strongly nil radical and other radicals of Г-rings. In view of these relations, we see that the quasi-strongly nil radical is a new radical in the radical theory of Г-rings.