  For any root system $\Delta$ and an irreducible representation ${\cal R}$ of
the reflection (Weyl) group $G_\Delta$ generated by $\Delta$, a {\em spin
Calogero-Moser model} can be defined for each of the potentials: rational,
hyperbolic, trigonometric and elliptic. For each member $\mu$ of ${\cal R}$, to
be called a "site", we associate a vector space ${\bf V}_{\mu}$ whose element
is called a "spin". Its dynamical variables are the canonical coordinates
$\{q_j,p_j\}$ of a particle in ${\bf R}^r$, ($r=$ rank of $\Delta$), and spin
exchange operators $\{\hat{\cal P}_\rho\}$ ($\rho\in\Delta$) which exchange the
spins at the sites $\mu$ and $s_{\rho}(\mu)$. Here $s_\rho$ is the reflection
generated by $\rho$. For each $\Delta$ and ${\cal R}$ a {\em spin exchange
model} can be defined. The Hamiltonian of a spin exchange model is a linear
combination of the spin exchange operators only. It is obtained by "freezing"
the canonical variables at the equilibrium point of the corresponding classical
Calogero-Moser model. For $\Delta=A_r$ and ${\cal R}=$ vector representation it
reduces to the well-known Haldane-Shastry model. Universal Lax pair operators
for both spin Calogero-Moser models and spin exchange models are presented
which enable us to construct as many conserved quantities as the number of
sites for {\em degenerate} potentials.
