Two-body decomposition processes of methylacetylene (CH(3)CCH) and its isotopomer methyl-d(3)-acetylene (CD(3)CCH) in intense laser fields (790 nm, 40 fs, 5.0 × 10(13) W cm(-2)) are investigated by the coincidence momentum imaging (CMI). In methyl-d(3)-acetylene, a total of six decomposition pathways in which one of the C-C bonds is broken and a total of six pathways in which an atomic hydrogen ion (H(+) or D(+)) or a molecular hydrogen ion (H(2)(+), HD(+), D(3)(+), or HD(2)(+)) is ejected are identified. It is revealed from the analysis of the CMI data that the migration of two deuterons as well as the exchange between a proton and a deuteron occurs prior to the two-body decomposition of a doubly charged parent molecule.