  We have carried out a study of the chemical abundances of $^1$H, $^4$He,
$^{12}$C, $^{13}$C, $^{14}$N, $^{15}$N, $^{16}$O, $^{17}$O, $^{20}$Ne and
$^{22}$Ne in symbiotic stars (SSs) by means of a population synthesis code. We
find that the ratios of the number of O-rich SSs to that of C-rich SSs in our
simulations are between 3.4 and 24.1, depending on the third dredge-up
efficiency $\lambda$ and the terminal velocity of the stellar wind $v(\infty)$.
The fraction of SSs with $extrinsic$ C-rich cool giants in C-rich cool giants
ranges from 2.1% to 22.7%, depending on $\lambda$, the common envelope
algorithm and the mass-loss rate. Compared with the observations, the
distributions of the relative abundances of $^{12}$C/$^{13}$C vs. [C/H] of the
cool giants in SSs suggest that the thermohaline mixing in low-mass stars may
exist. The distributions of the relative abundances of C/N vs. O/N, Ne/O vs.
N/O and He/H vs. N/O in the symbiotic nebulae indicate that it is quite common
that the nebular chemical abundances in SSs are modified by the ejected
materials from the hot components. Helium overabundance in some symbiotic
nebulae may be relevant to a helium layer on the surfaces of white dwarf
accretors.
