The cross sections for exclusive DD and DD meson pair production in peripheral nucleus-nucleus collisions are calculated and several differential distributions are presented. The calculation of the elementary γγ→DDbar 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 γγ→DDbar cross sections.