We present an ab initio plane-wave-pseudopotential investigation of Si- (Ge-)capped Ge (Si) nanocrystallites. The effects of capping Si and Ge nanocrystallites on the electron-hole pair excitation energies, optical absorption spectra, localization of the highest-occupied and lowest-unoccupied molecular orbitals, Stokes shifts, and radiative lifetimes are analyzed. The bond lengths and the localization of electrons and holes in the Si- (Ge-)capped nanocrystallites are similar to those found in the analogous $\mathrm{Si}∕\mathrm{Ge}$ heterostructures. Due to the changes in the quantum confinement properties caused by the capping, there are significant differences in the electronic and optical properties of Ge-capped Si nanocrystallites and Si-capped Ge nanocrystallites.