  The Toda lattice (TL) hierarchy was first introduced by K.Ueno and K.Takasaki
in \cite{uenotaksasai} to generalize the Toda lattice equations\cite{toda}.
Along the work of E. Date, M. Jimbo, M. Kashiwara and T. Miwa \cite{DJKM} on
the KP hierarchy, K.Ueno and K.Takasaki in \cite{uenotaksasai} develop the
theory for the TL hierarchy: its algebraic structure, the linearization, the
bilinear identity, $\tau$ function and so on. Also the analogues of the B and C
types for the TL hierarchy, i.e. the BTL and CTL hierarchies, are considered in
\cite{uenotaksasai}, which are corresponding to infinite dimensional Lie
algebras $\textmd{o}(\infty)$ and $\textmd{sp}(\infty)$ respectively. In this
paper, we will focus on the study of the additional symmetries for the BTL and
CTL hierarchies.
