Let $T $ be a bounded linear operator on a complex Hilbert space 

with the polar decomposition $ T = U \vert T \vert $.

 Let $T(t) = \vert T \vert^{t} U \vert T \vert^{1-t} $ for 

$ 0 < t < 1, T(0) = U^{*}UU \vert T \vert$ and 

$ T(1) = \vert T \vert U$. 

$T(t)$ is called Aluthge 

transform of $T$. In this paper, we investigate spectral relations 

between $T$ and $T(t)$. For example, we prove that $T$ and $T(t)$ 

have the same essential spectrum and Weyl spectrum, and prove that 

 Weyl's theorem holds for $T$ if and only if Weyl's theorem holds 

for $T(t)$.