  Let $(G,H,\sigma)$ be a symmetric pair and
$\mathfrak{g}=\mathfrak{m}\oplus\mathfrak{h}$ the canonical decomposition of
the Lie algebra $\mathfrak{g}$ of $G$. We denote by ${\nabla}^0$ the canonical
affine connection on the symmetric space $G/H$. A torsion-free $G$-invariant
affine connection on $G/H$ is called special if it has the same curvature as
${\nabla}^0$. A special product on $\mathfrak{m}$ is a commutative,
associative, and ${\operatorname{Ad}}(H)$-invariant product. We show a
one-to-one correspondence between the set of special affine connections on
$G/H$ and the set of special products on $\mathfrak{m}$. We introduce a
subclass of symmetric pairs called strongly semi-simple for which we prove that
the canonical affine connection on $G/H$ is the only special affine connection,
and we give many examples. We study a subclass of commutative, associative
algebra, allowing us to give examples of symmetric spaces with special affine
connections. Finally, we compute the holonomy Lie algebra of special affine
connections.
