  We locate all of the zeros of certain Poincare series associated with the
Fricke groups $\Gamma_0^*(2)$ and $\Gamma_0^*(3)$ in their fundamental domains
by applying and extending the method of F. K. C. Rankin and H. P. F.
Swinnerton-Dyer (``On the zeros of Eisenstein series'', 1970).
