  The orthogonal polynomials with recurrence relation \[(\la\_n+\mu\_n-z)
F\_n(z)=\mu\_{n+1} F\_{n+1}(z)+\la\_{n-1} F\_{n-1}(z)\] with two kinds of cubic
transition rates $\la\_n$ and $\mu\_n,$ corresponding to indeterminate
Stieltjes moment problems, are analyzed. We derive generating functions for
these two classes of polynomials, which enable us to compute their Nevanlinna
matrices. We discuss the asymptotics of the Nevanlinna matrices in the complex
plane.
