The article deals with the problematic of the on—their—own learners’ work in the school instruction which is organized on the principles of the new conception on the base of the developing teaching. During the last, appropriately 20 years, some authors of pedagogical papers have been involved in the problematic of the on—their—own work of pupils. The article presents a partly survey of the authors’ definitions, whose analysis became the foundation of their own classification of the term dealt with. On the example of experimental teaching of Š. A. Amonašvili he tries to demonstrate the problematic of the on—their—own work variety of teaching in Gruzia, the problem itself not being really elaborated so far. — This conception will enable a new view of the place and function of the on—their—own work of pupils in the instruction of the future. In connection with the problematic of individual stages of that type of work types of reproductional, reconstructional, and creative work were made clear here. In the analysis of the learners’ on— their—own work even the algorythmisized learners’ activity was put into connection with the learners’ independency and their capability of the type of work dealt with here. In the conclusion of the work the place of the on—their—own work of the pupils in the modern teaching is being emphasized.