  The D-dimensional conformal nonlinear sigma-models (NSM) sre constructed. It
is shown that the NSM on spaces with $\pi_{D-1} = \mathbb {Z}$ have the
topological solutions of a "hedgehog" and "anti-hedgehog" types with
logarithmic energies. For spaces with $\pi_D \ne 0$ they have also the
topological excitations of instanton types with finite energies.
