  We derive the relativistic formulas for the van der Waals coefficients of
Yb-alkali dimers that correlate to ground and excited separated-atom limits. We
calculate $C_6$ and $C_8$ coefficients of particular experimental interest. We
also derive a semi-empirical formula that expresses the $C_8$ coefficient of
heteronuclear $A+B$ dimers in terms of the $C_6$ and $C_8$ coefficients of
homonuclear dimers and the static dipole and quadrupole polarizabilities of the
atomic states $A$ and $B$. We report results of calculation of the $C_6$
coefficients for the Yb-Rb $^3/!P_1^o+5s\, ^2/!S_{1/2}$ and $^1/!S_0+5p\,
^2/!P^o_{1/2}$ dimers, and the $C_8$ coefficients for the Yb-Li $^1/!S_0+2s\,
^2/!S_{1/2}$ and Yb-Rb $^1/!S_0+5s\, ^2/!S_{1/2}$ dimers. Uncertainties are
estimated for all predicted properties.
