  Photoproduction of $\pi^0\pi^{\pm}$-pairs from quasifree nucleons bound in
the deuteron has been investigated to study the helicity dependence of this
reaction. Measurements with a liquid deuterium target were used to extract the
unpolarized cross sections for reactions on protons and neutrons. A deuterated,
longitudinally polarized solid-butanol target, together with a circularly
polarized photon beam, determined the double polarization observable $E$. From
these results the spin-dependent cross sections $\sigma_{1/2}$ and
$\sigma_{3/2}$, corresponding to the anti-parallel and parallel spin
configurations of the beam photon and target nucleon, have been derived. The
measurements were performed at the Mainz MAMI accelerator with tagged,
circularly-polarized photon beams produced via bremsstrahlung from
longitudinally polarized electron beams. The reaction products were detected
with an almost $4\pi$ solid-angle covering calorimeter composed of the Crystal
Ball and TAPS detectors, supplemented by plastic scintillation detectors for
charged particle identification. The results are sensitive to sequential decays
of nucleon resonances via intermediate states and also to the decay of nucleon
resonances by emission of charged $\rho$ mesons, and are compared to recent
model results.
