  The article deals with iterative methods of solving linear operator equations
$x = Bx + f$ and $Ax = f$ with self-adjoint operators in Hilbert space $X$ in
critical case when $\rho(B) = 1$ and $0 \in {\rm Sp}\, A$. The main results are
based on the use of M.A. Krasnosel'ski\u{i} theorem about the convergence of
the successive approximations and some its modifications and refinements.
