Summary: The Sobolev type equations are studied quite complete in Banach spaces. Quasi-Sobolev spaces are quasi normalized complete spaces of sequences. Recently the Sobolev type equations began to be studied in these spaces. The paper is devoted to the study of boundary on axis solutions for the Barenblatt-Zheltov-Kochina model. { }Apart from the introduction and bibliography the paper contain two parts. The first one gives preliminary information about the properties of operators in quasi Banach spaces, as well as about the relatively bounded operator. The second part gives main result of the paper about boundary on axis solutions for the Barenblatt-Zheltov-Kochina model in quasi-Sobolev spaces. Note that reference list reflects the tastes of the author and can be supplemented.