  Let $X$ be the Cantor set and $\phi$ be a minimal homeomorphism on
$X\times\T$. We show that the crossed product $C^*$-algebra
$C^*(X\times\T,\phi)$ is a simple $A\T$-algebra provided that the associated
cocycle takes its values in rotations on $\T$. Given two minimal systems
$(X\times\T,\phi)$ and $(Y\times\T,\psi)$ such that $\phi$ and $\psi$ arise
from cocycles with values in isometric homeomorphisms on $\T$, we show that two
systems are approximately $K$-conjugate when they have the same $K$-theoretical
information.
