The fragmentation dynamics of allene and propyne molecules following photoexcitation at 203.3, 209.0 and 213.3 nm have been investigated by H (Rydberg) atom photofragment translational spectroscopy methods. Contrary to conclusions reached in previous photochemical studies of these molecules, at a photolysis wavelength of 193 nm, we find the translational energy spectra associated with the H atom product forming channel in both molecules to be essentially identical, and to have a form that is reproduced well by an approximate statistical model that assumes population of all possible vibrational states of the H2CCCH partner. Such behavior can be most readily accommodated by assuming that, for both molecules, at the excitation energies used in the present work, internal conversion to, and isomerization on, the ground state potential energy surface precedes fragmentation.