  The beam-recoil double polarization P_{x'}^h and P_{z'}^h and the recoil
polarization P_{y'} were measured for the first time for the
p(\vec{e},e'\vec{p})\eta reaction at a four-momentum transfer of Q^2=0.1
GeV^2/c^2 and a center of mass production angle of \theta = 120^\circ at MAMI
C. With a center of mass energy range of 1500 MeV < W < 1550 MeV the region of
the S_{11}(1535) and D_{13}(1520) resonance was covered. The results are
discussed in the framework of a phenomenological isobar model (Eta-MAID). While
P_{x'}^h and P_{z'}^h are in good agreement with the model, P_{y'} shows a
significant deviation, consistent with existing photoproduction data on the
polarized-target asymmetry.
