Key polynomials and preminimal pairs

The paper is in theory of valued fields and devoted to questions of describing extentions valuations of a field on its field of rational functions in one variable.One of effective tools for descriptions of such extentions is the notion of key polynomial introduced by S,Maclane in 1936 year.Using the notion of preminimal pair introduced recently new characterisation of key polynomials over henselian fields was obtained.