  We introduce the spectral points of two-sided positive type of bounded normal
operators in Krein spaces. It is shown that a normal operator has a local
spectral function on sets which are of two-sided positive type. In addition, we
prove that the Riesz-Dunford spectral subspace corresponding to a spectral set
which is only of positive type is uniformly positive. The restriction of the
operator to this subspace is then normal in a Hilbert space.
