Photoproduction of $pieta$-pairs from nucleons has been investigated from threshold up to incident photon energies of $approx$~1.4~GeV. The quasi-free reactions $gamma prightarrow ppi^0eta$, $gamma nrightarrow npi^0eta$, $gamma prightarrow npi^+eta$, and $gamma nrightarrow ppi^-eta$ were for the first time measured from nucleons bound in the deuteron. The corresponding reactions from a free-proton target were also studied to investigate final-state interaction effects (for neutral pions the free-proton results could be compared to previous measurements; the $gamma prightarrow npi^+eta$ reaction was measured for the first time). For the $pi^0eta$ final state coherent production via the $gamma drightarrow dpi^0eta$ reaction was also investigated. The experiments were performed at the tagged photon beam of the Mainz MAMI accelerator using an almost $4pi$ coverage electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. The total cross sections for the four different final states obey the relation $sigma(ppi^0eta)$ $approx$ $sigma(npi^0eta)$ $approx$ $2sigma(ppi^-eta)$ $approx$ $2sigma(npi^+eta)$ as expected for a dominant contribution from a $Delta^{star}rightarrowetaDelta(1232)rightarrowpieta N$ reaction chain, which is also supported by the shapes of the invariant-mass distributions of nucleon-meson and $pi$-$eta$ pairs. The experimental results are compared to the predictions from an isobar reaction model.
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