During some years there was a research of properties of an observation telescope with non-ideal primary mirror and nonlinear optical correction of received images. Different schemes of reading out of the information about primary mirror distortions were investigated, various types of nonlinear correctors were used, and possible ways of creation of a telescope primary mirror with acceptable optical quality were investigated. Brief history of these researches will be given in this paper. The results of real-time holographic correction of image of a moving object observed by a telescope with a membrane primary 300 mm in a diameter will be also discussed.