  This paper is devoted to the investigation of the Weyl and the essential
$S-$spectrum of a bounded right quaternionic linear operator in a right
quaternionic Hilbert space. Using the quaternionic Riesz projection, the
$S-$eigenvalue of finite type is introduced and studied. In particular, it is
shown that the Weyl and the essential $S-$spectra does not contains eigenvalues
of finite type. We also describe the boundary of the Weyl $S-$spectrum and the
particular case of the spectral theorem of the essential $S-$spectrum.
