Consider the following Hamiltonian dynamical system:
where the Hamiltonian function is
. The classical KAM theorem asserts that if
is not degenerate i.e. det
then most of the invariant tori can persist when
is sufficiently small. In general, the nondegeneracy condition is necessary for KAM theorems. However, the Hamiltonian systems with two degrees of freedom have some special properties and so, the present paper is devoted to a KAM theorem for a class of 2D Hamiltonian systems without any nondegeneracy condition. The main tool is the so-called KAM iteration.