Laser photofragmentation of Si, Ge, and GaAs positive cluster ions prepared by laser vaporization and supersonic beam expansion has been investigated in a tandem time-of-flight mass spectrometer. Si\sbn\sp+ up to size 80, Ge\sbn\sp+ and Ga\sbxAs\sby\sp+ up to a total of 31 atoms have been studied. Ga\sbxAs\sby\sp+ fragment in a nearly uniform pattern probably via a step-loss of atoms pattern with odd fragments being more prominent than their even neighbors. Both Si\sbn\sp+ and Ge\sbn\sp+ of all sizes show as one fragmentation channel loss of one atom to produce Si\sbn−1\sp+ or Ge\sbn−1\sp+. In addition, Si\sbn\sp+ and Ge\sbn\sp+ in the size range n = 10-30 photofragment to produce positive ions of about one half the mass of the parent. For Ge\sbn\sp+ as n becomes greater than 30, this fragmentation becomes a pattern in which positive ions containing 10 (or 7) fewer atoms are the principal products at low laser fluence. Increased fluence seems to fragment these daughters in the same way as they would behave as primary ions. The Si\sbn\sp+ ions of greater than 30 atoms do not show this 10 or 7 atom neutral loss. Both Si\sbn\sp+ and Ge\sbn\sp+ for n > 30 show an additional channel in which small positive ion fragments in the n = 6 to 11 size range are produced. This channel requires high fluence and is shown to involve at least two 6.4 eV (ArF) photons for Si\sb60\sp+. The absence of intermediate fragments in this channel suggests that these large cluster ions break down into several clusters because the positive charge would be expected to stay with the larger fragment in a fission into two clusters as the ionization potentials of the neutral clusters decrease with size. A reflectron tandem time-of-flight mass spectrometer has been designed and constructed. The resultant high resolution makes the apparatus a highly efficient instrument for fragmentation and spectroscopic studies.