We study interference effects that appear in the cross section due to detection of two indistinguishable electrons in a photoelectron--Auger-electron pair (intrachannel exchange interference), or due to detection of two indistinguishable photoelectron-Auger electron pairs that share the final state but are emitted via two different intermediate states (interchannel exchange interference). For photoinduced Kr ${M}_{4,5}$--${N}_{1}{N}_{23}$ (Xe $N$${}_{4,5}$--${O}_{1}{O}_{23}$) Auger decay, the intrachannel exchange interference is ``switched on'' at 131.3 eV (87.0 eV) and 133.8 eV (91.0 eV) photon impact energy for the ${M}_{5}$ (${N}_{5}$) and ${M}_{4}$ (${N}_{4}$) holes, respectively. The interchannel exchange interference is expected to appear at 132.6 eV (89.0 eV) when the photoelectron ejected from the ${M}_{4}$ (${N}_{4}$) subshell is emitted with the same energy as the Auger electron emitted in the decay of the ${M}_{5}$ (${N}_{5}$) hole, and vice versa, the energy of the photoelectron ejected from the ${M}_{5}$ (${N}_{5}$) subshell equals the energy of the Auger electron emitted in the decay of the ${M}_{4}$ (${N}_{5}$) hole. We use the approach of Vegh and Macek [Phys. Rev. A 50, 4031 (1994)], and Vegh [Phys. Rev. A 50, 4036 (1994)] to model these phenomena in a unified manner and examine their effects in an angle-resolved and angle-integrated coincidence spectra considering also the postcollision interaction (PCI). The previous and the present angle-resolved experimental results, together with the data obtained by a magnetic bottle time-of-flight spectrometer, indicate that in this particular case the exchange interference effects in the angle-integrated cross sections are considerably weaker than in the angle-resolved $(\ensuremath{\gamma},2e)$ cross sections.