  By an explicit calculation we demonstrate that the triple gauge-ghost
vertices in a general renormalizable ${\cal N}=1$ supersymmetric gauge theory
are UV finite in the two-loop approximation. For this purpose we calculate the
two-loop divergent contribution to the $\bar c^+ V c$-vertex proportional to
$(C_2)^2$ and use the finiteness of the two-loop contribution proportional to
$C_2 T(R)$ which has been checked earlier. The theory under consideration is
regularized by higher covariant derivatives and quantized in a manifestly
${\cal N}=1$ supersymmetric way with the help of ${\cal N}=1$ superspace. The
two-loop finiteness of the vertices with one external line of the quantum gauge
superfield and two external lines of the Faddeev--Popov ghosts has been
verified for a general $\xi$-gauge. This result agrees with the
nonrenormalization theorem proved earlier in all orders, which is an important
step for the all-loop derivation of the exact NSVZ $\beta$-function.
