The cross sections for exclusive D + D − and D 0 ¯ D0 meson pair production in peripheral nucleus - nucleus collisions are calculated and several differential distributions are presented. The calculation of the elementary ! D ¯ 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. 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 ! D ¯ D cross sections.