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By an explicit calculation we demonstrate that the triple gauge-ghostvertices in a general renormalizable ${\cal N}=1$ supersymmetric gauge theoryare UV finite in the two-loop approximation. For this purpose we calculate thetwo-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 isregularized by higher covariant derivatives and quantized in a manifestly${\cal N}=1$ supersymmetric way with the help of ${\cal N}=1$ superspace. Thetwo-loop finiteness of the vertices with one external line of the quantum gaugesuperfield and two external lines of the Faddeev--Popov ghosts has beenverified for a general $\xi$-gauge. This result agrees with thenonrenormalization theorem proved earlier in all orders, which is an importantstep for the all-loop derivation of the exact NSVZ $\beta$-function.

Finiteness of the triple gauge-ghost vertices in ${\cal N}=1$ supersymmetric gauge theories: the two-loop verification