The study of operators having some special spectral properties like Weyl's theorem, Browder's theorem
and the SVEP has been of important interest for some time now. The SVEP is very useful in the study of
the local spectral theory. In this paper, we explore the single-valued extension property (SVEP) for some
operators on Hilbert spaces. We characterize operators with or without SVEP at zero and those where
Weyl's and Browder's theorems hold. It is shown that if a Fredholm operator has no SVEP at zero, then
zero is an accumulation point of the spectrum of the operator. It is also shown that quasi similar Fredholm
operators have equal Weyl spectrum.