Formation of a bilayer or a multilayer organic thin film on semiconductor surfaces is promising for the manufacture of new-generation microelectronic/nanoelectronic materials. A prerequisite for realization of such a goal is the formation of monolayer organic thin films with reactive functional groups exposed as a template for further chemical manipulations. We report herein a theoretical prediction that attachments of diacetylenes on Si(100)-2 x 1, Ge(100)-2 x 1, and Si(111)-7 x 7 surfaces could produce monolayers of reactive [3]cumulenic or/and enynic surface species. Our density-functional cluster-model calculations revealed the following: (i) Diacetylene can undergo either stepwise [4 + 2]-like or stepwise [2 + 2]-like cycloadditions onto a X=X dimer of X(100)-2 x 1 surfaces (X = Si and Ge) via a common singlet-diradical intermediate. (ii) On Si(100), the [2 + 2]-like pathway is kinetically favored over the [4 + 2]-like one, preferentially giving rise to enynic adspecies. (iii) On Ge(100), both pathways are competitive, resulting concomitantly in [3]cumulenic and enynic adspecies. (iv) On Si(111)-7 x 7, diacetylene can undergo either 1,4 addition or 1,2 addition onto a rest atom-adatom pair with the former process being favored over the latter both thermodynamically and kinetically and leading preferentially to the formation of [3]cumulenic adspecies on the surface. It is noteworthy that the [4 + 2]-like cycloaddition of diacetylene on Ge(100) 2 x 1 is among the few examples of [4 + 2] cycloaddition with a 1,3-diyne acting as a four-electron component affording six-membered cyclic [3]cumulenes.