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The paper is devoted to the problem of finding free generators in the fieldsof invariants for actions of unipotent groups on affine varieties. We considerthe case when the unipotent group is the unipotent radical in an arbitraryparabolic subgroup in the reductive group of classical type GL(n), SL(n), O(n)or Sp(2n). In the explicit form, we present a system of free generators in thefield of invariants for the action of the unipotent radical on the reductivegroup by conjugation.

Fields of invariants for unipotent radicals of parabolic subgroups