  A nonlinear operator equation $F(x)=0$, $F:H\to H,$ in a Hilbert space is
considered. Continuous Newton's-type procedures based on a construction of a
dynamical system with the trajectory starting at some initial point $x_0$ and
becoming asymptotically close to a solution of $F(x)=0$ as $t\to +\infty$ are
discussed. Well-posed and ill-posed problems are investigated.
