Peter Petrov Title: Some theorems of Zariski – van Kampen type Abstract: After a brief history of Zariski – van Kampen theorem, the relative version of the homotopical variation operator is defined, permitting its generalization proposed by Eyral. The main result of this talk is a further generalization of the latter, giving at the same time partial answer to the conjecture of Chéniot – Eyral.