  We perform a systematic search for anti-de Sitter vacua of maximal
supergravity with N>2 residual supersymmetries. We find that maximal
supergravity admits two 1-parameter classes of N=3 and N=4 vacua, respectively.
They are embedded, for the different values of an angular parameter, in the
$\omega$-rotated SO(8) (N=3) and SO(1,7) (N=4 and 3) gauged models. All vacua
disappear in the limit when $\omega$ tends to zero. We determine the mass
spectra and the AdS-supermultiplet structure. These appear to be the first and
only N>2 supersymmetric AdS vacua in maximal supergravity, aside from the N=8
vacua of the SO(8)-gauged models. We also prove on general grounds that no such
vacua can exist for 4<N<8.
