  The generalized Henon-Heiles system with an additional nonpolynomial term is
considered. In two nonintegrable cases new two-parameter solutions have been
obtained in terms of elliptic functions. These solutions generalize the known
one-parameter solutions. The singularity analysis shows that it is possible
that three-parameter single-valued solutions exist in these two nonintegrable
cases. The knowledge of the Laurent series solutions simplifies search of the
elliptic solutions and allows to automatize it.
