  We study the behavior of zero-divisors of the double zeta-function
$\zeta_2(s_1,s_2)$. In our former paper \cite{MatSho14} we studied the case
$s_1=s_2$, but in the present paper we consider the more general two variable
situation. We carry out numerical computations in order to trace the behavior
of zero-divisors. We observe that some divisors approach the points with
$s_2=0$, while other divisors approach the points which are solutions of
$\zeta(s_2)=1$.
