  Consider an operator equation (*) $B(u)-f=0$ in a real Hilbert space.
  Let us call this equation ill-posed if the operator $B'(u)$ is not boundedly
invertible, and well-posed otherwise. The DSM (dynamical systems method) for
solving equation (*) consists of a construction of a Cauchy problem, which has
the following properties:
  1) it has a global solution for an arbitrary initial data,
  2) this solution tends to a limit as time tends to infinity,
  3) the limit is the minimal-norm solution to the equation $B(u)=f$.
  A global convergence theorem is proved for DSM for equation (*) with monotone
$C_{loc}^2$ operators $B$.
