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The paper is devoted to a computation of the Lie superalgebras of holomorphicvector fields on isotropic flag supermanifolds of maximal type corresponding tothe Lie superalgebras $\mathfrak{osp}_{2m|2n}(\mathbb C)$ and$\pi\mathfrak{sp}_{n}(\mathbb C)$. The result is that under some restrictionson the flag type any holomorphic vector field is fundamental with respect tothe natural action of the Lie superalgebras $\mathfrak{osp}_{2m|2n}(\mathbb C)$or $\pi\mathfrak{sp}_{n}(\mathbb C)$.

Vector fields on $\mathfrak{osp}_{2m|2n}(\mathbb C)$- and $\pi\mathfrak{sp}_{n}(\mathbb C)$-flag supermanifolds