  The classical problem of construction of Gardner's deformations for
infinite-dimensional completely integrable systems of evolutionary partial
differential equations (PDE) amounts essentially to finding the recurrence
relations between the integrals of motion. Using the correspondence between the
zero-curvature representations and Gardner deformations for PDE, we construct a
Gardner's deformation for the Krasil'shchik-Kersten system. For this, we
introduce the new nonlocal variables in such a way that the rules to
differentiate them are consistent by virtue of the equations at hand and
second, the full system of Krasil'shchik-Kersten's equations and the new rules
contains the Korteweg-de Vries equation and classical Gardner's deformation for
it.
  PACS: 02.30.Ik, 02.30,Jr, 02.40.-k, 11.30.-j
