  Isabel Martin-Lyons and Paul J.Truman generalized the definition of a skew
brace to give a new algebraic object, which they termed a skew bracoid. Their
construction involves two groups interacting in a manner analogous to the
compatibility condition found in the definition of a skew brace. They
formulated tools for characterizing and classifying skew bracoids, and studied
substructures and quotients of skew bracoids. In this paper we study two-sided
bracoids. In \cite{WR07} Rump showed that if a left brace $(B, \star ,\cdot )$
is a two-sided brace and the operation $\ast : B \times B \longrightarrow B$ is
defined by $a \ast b = a\cdot b \star \overline{a} \star \overline{b}$ for all
$a, b \in B$ then $(B, \star ,\ast )$ is a Jacobson radical ring. Lau showed
that if $(B, \star ,\cdot )$ is a left brace and the operation is asssociative,
then $B$ is a two-sided brace. We will prove bracoid versions of this results.
