  A \emph{$[z, r; g]$-mixed cage} is a mixed graph $z$-regular by arcs,
$r$-regular by edges, with girth $g$ and minimum order. %In this paper we study
structural properties of mixed cages: Let $n[z,r;g]$ denote the order of a
$[z,r;g]$-mixed cage. In this paper we prove that $n[z,r;g]$ is a monotonicity
function, with respect of $g$, for $z\in \{1,2\}$, and we use it to prove that
the underlying graph of a $[z,r;g]$-mixed cage is 2-connected, for $z\in
\{1,2\}$. We also prove that $[z,r;g]$-mixed cages are strong connected. We
present bounds of $n[z,r;g]$ and constructions of $[z,r;5]$-mixed graphs and
show a $[10,3;5]$-mixed cage of order $50$.
