  It is shown that the classical L-operator algebra of the elliptic
Ruijsenaars-Schneider model can be realized as a subalgebra of the algebra of
functions on the cotangent bundle over the centrally extended current group in
two dimensions. It is governed by two dynamical r and $\bar{r}$-matrices
satisfying a closed system of equations. The corresponding quantum R and
$\overline{R}$-matrices are found as solutions to quantum analogs of these
equations. We present the quantum L-operator algebra and show that the system
of equations on R and $\overline{R}$ arises as the compatibility condition for
this algebra. It turns out that the R-matrix is twist-equivalent to the Felder
elliptic R^F-matrix with $\overline{R}$ playing the role of the twist. The
simplest representation of the quantum L-operator algebra corresponding to the
elliptic Ruijsenaars-Schneider model is obtained. The connection of the quantum
L-operator algebra to the fundamental relation RLL=LLR with Belavin's elliptic
R matrix is established. As a byproduct of our construction, we find a new
N-parameter elliptic solution to the classical Yang-Baxter equation.
