  To begin with, we study $\mathcal{O}$-operators of pre-Malcev and symmetric
solutions of the analogue classical Yang-Baxter equation(CYBE). We show that a
symmetric solution of the analogue CYBE can be interpreted as an
$\mathcal{O}$-operator associated to the co-regular bimodule. We also show that
$\mathcal{O}$-operators associative to a general bimodule give rise to
symmetric solutions of the analogue of CYBE in certain semi-direct product
pre-Malcev algebra. Next, we study infinitesimal deformations of a pre-Malcev
algebra and introduce the notion a Nijenhuis pair, which gives a trivial
deformation associative to a bimodule. We introduce the definition of an
$\mathcal{O}$-dual-$\mathcal{N}$ structures on pre-Malcev algebra with a
bimodule. We show that an $\mathcal{O}$-(dual-)$\mathcal{N}$ structure can give
an $\mathcal{O}$-operator and conversely an $\mathcal{O}$-(dual-)$\mathcal{N}$
structure can give rise to a hierarchy of pairwise compatible
$\mathcal{O}$-operators of a pre-Malcev algebra. Finally, we introduce the
notations of an r-$\mathcal{N}$ structure and a $\mathcal{B}$-$\mathcal{N}$
structure as two special cases of an $\mathcal{O}$-dual-$\mathcal{N}$
structure. We reveal relationships between compatible r-matrices and a
$\mathcal{B}$-$\mathcal{N}$ structure on pre-Malcev algebra.
