The life cycle of the population of interstellar polycyclic aromatic hydrocarbon (PAH) molecules depends partly on the photostability of the individual species. We have studied the dissociative photoionization of two ethynyl-substituted PAH species, namely, 9-ethynylphenanthrene and 1-ethynylpyrene. Their adiabatic ionization energy and the appearance energy of fragment ions have been measured with the photoelectron photoion coincidence (PEPICO) spectroscopy technique. The adiabatic ionization energy has been found at 7.84 +/- 0.02 eV for 9-ethynylphenanthrene and at 7.41 +/- 0.02 eV for 1-ethynylpyrene. These values are similar to those determined for the corresponding non-substituted PAH molecules phenanthrene and pyrene. The appearance energy of the fragment ion indicative of the loss of a H atom following photoionization is also similar for either ethynyl-substituted PAH molecule and its non-substituted counterpart. The measurements are used to estimate the critical energy for the loss of a H atom by the PAH cations and the stability of ethynyl-substituted PAH molecules upon photoionization. We conclude that these PAH derivatives are as photostable as the non-substituted species in HI regions. If present in the interstellar medium, they may play an important role in the growth of interstellar PAH molecules.