The Born-Oppenheimer type separation between light and heavy nuclear motions is applied to the study of the dynamics of the ClHCl and ClDCl systems. Approximate and elaborate approaches are used to calculate the photodetachment spectra of the ClHCl- and ClDCl- anions. The approximate approach is based on a Born-Oppenheimer approximation where the nuclear wave function of the ClHCl or ClDCl systems is obtained as a single product of two wave functions which describe the motion of the light H(D) nucleus for clamped chlorine nuclei and the motion of the heavy chlorine nuclei, respectively. The elaborate approach is a multistate description which goes beyond the Born-Oppenheimer approximation. The relevant close coupling equations are solved numerically subject to proper photodissociation asymptotic conditions. The results obtained in this approach confirm the validity of the approximate one and provide additional information on the ClH + Cl and ClD + Cl decay channels. Resonances are obtained at energies of 0.640 eV and 0.899 eV for the ClHCl system, and at 0.538 eV and 0.715 eV for the ClDCl system. They are identified as shape or Feshbach resonances and analyzed in terms of the normal modes of a linear symmetrical triatomic molecule.