  In this paper, we obtain a full classification of reductive dual pairs in a,
real or complex, Lie superalgebra $\mathfrak{spo}(E)$ and Lie supergroup
$\textbf{SpO}(E)$. Moreover, by looking at the natural action of the
orthosymplectic Lie supergroup $\textbf{SpO}(E)$ on the Weyl-Clifford algebra
$\textbf{WC}(E)$, we prove that for a reductive dual pair $(\mathscr{G}\,,
\mathscr{G}') = ((G\,, \mathfrak{g})\,, (G'\,, \mathfrak{g}'))$ in
$\textbf{SpO}(E)$, the superalgebra $\textbf{WC}(E)^{\mathscr{G}}$ consisting
of $\mathscr{G}$-invariant elements in $\textbf{WC}(E)$ is generated by the Lie
superalgebra $\mathfrak{g}'$.
  We obtain a full classification of reductive dual pairs in the (real or
complex) Lie superalgebra $\mathfrak{spo}(\mathrm E)$ and the Lie supergroup
$\textbf{SpO}(\mathrm E)$. Using this classification we prove that for a
reductive dual pair $(\mathscr{G}\,, \mathscr{G}') = ((\mathrm G\,,
\mathfrak{g})\,, (\mathrm G'\,, \mathfrak{g}'))$ in $\textbf{SpO}(\mathrm E)$,
the superalgebra $\textbf{WC}(\mathrm E)^{\mathscr{G}}$ consisting of
$\mathscr{G}$-invariant elements in the Weyl-Clifford algebra
$\textbf{WC}(\mathrm E)$, equipped with the natural action of the
orthosymplectic Lie supergroup $\textbf{SpO}(\mathrm E)$, is generated by the
Lie superalgebra $\mathfrak{g}'$.
  As an application, we prove that Howe duality holds for the dual pairs
$({\textbf{SpO}}(2n|1)\,, {\textbf{OSp}}(2k|2l)) \subseteq
{\textbf{SpO}}(\mathbb{C}^{2k|2l} \otimes \mathbb{C}^{2n|1})$.
