  In this paper we extend the transfer operator approach to Selberg's zeta
function for cofinite Fuchsian groups to the Hecke triangle groups G_q,
q=3,4,..., which are non-arithmetic for q \not= 3,4,6. For this we make use of
a Poincare map for the geodesic flow on the corresponding Hecke surfaces which
has been constructed in arXiv:0801.3951 and which is closely related to the
natural extension of the generating map for the so called Hurwitz-Nakada
continued fractions. We derive simple functional equations for the
eigenfunctions of the transfer operator which for eigenvalues rho =1 are
expected to be closely related to the period functions of Lewis and Zagier for
these Hecke triangle groups.
