Let $T$ be a bounded linear operator 
on a complex Hilbert space $\mathcal{H}$. $T$ is called $(p,k)$-quasihyponormal 
if $ T^{*}( (T^*T)^p - (TT^*)^p) T \geq   0 $ for $ 0 < p \leq 1$ and $k \in 
{\mathbb N}$.  In this paper, we prove Weyl type theorems
for $(p,k)$-hyponormal operators. Especially, 
we prove that generalized $a$-Weyl's theorem holds for $T$ if $T^{*}$ is 
$(p,k)$-quasihyponormal.