  Let $F$ be an algebraically closed field of zero characteristic. If the
transcendence degree of $F$ over $\mathbb{Q}$ is finite, then all Chevalley
groups over $F$ are known to possess the $R_{\infty}$-property. If the
transcendence degree of $F$ over $\mathbb{Q}$ is infinite, then Chevalley
groups of type $A_n$ over $F$ do not possess the $R_{\infty}$-property. In the
present paper, we consider Chevalley groups of classical series $B_n$, $C_n$,
$D_n$ over $F$ in the case when the transcendence degree of $F$ over
$\mathbb{Q}$ is infinite, and prove that such groups do not possess the
$R_{\infty}$-property.
