  In the aspon model solution of the strong $CP$ problem, there is a gauged
$U(1)$ symmetry, spontaneously broken by the same vacuum expectation value
which breaks $CP$, whose massive gauge boson provides an additional mechanism
of weak $CP$ violation. We calculate the $CP$ asymmetries in $B$ decays for the
aspon model and show that they are typically smaller than those predicted from
the standard model. A linear relation between the $CP$ asymmetries of different
decay processes is obtained.
