  The cross sections for exclusive $D^+D^-$ and $D^0 \bar {D^0}$ meson pair
production in peripheral nucleus - nucleus collisions are calculated and
several differential distributions are presented. The calculation of the
elementary $\gamma \gamma \to D \bar D$ cross section is done within the
heavy-quark approximation and in the Brodsky- Lapage formalism with
distribution amplitudes describing recent CLEO data on leptonic $D^+$ decay.
Realistic (Fourier transform of charge density) charge form factors of nuclei
are used to generate photon flux factors. Absorption effects are discussed and
quantified. The cross sections of a few nb are predicted for RHIC and of a few
hundreds of nb for LHC with details depending on the approximation made in
calculating elementary $\gamma \gamma \to D \bar D$ cross sections.
