  The generalized Henon-Heiles system has been considered. In two nonintegrable
cases with the help of the Painleve test new special solutions have been found
as Laurent series, depending on three parameters. The obtained series converge
in some ring. One of parameters determines the singularity point location,
other parameters determine coefficients of series. For some values of these
parameters the obtained Laurent series coincide with the Laurent series of the
known exact solutions. The Painleve test can be used not only to construct
local solutions as the Laurent series but also to find elliptic solutions.
