  We consider a dynamics of Higgs' field in the framework of cosmological
models involving the scalar field from Nonsymmetric Kaluza-Klein (Jordan-Thiry)
Theory. The field plays here a role of a quintessence field. We consider phase
transition in cosmological models of the second and of the first order due to
evolution of Higgs' field. We developed inflationary models including
calculation of an amount of inflation. We match some cosmological models,
calculating a Hubble parameter and an age of the Universe.
