  We discuss the nearest lambda_q--multiple continued fractions and their duals
for lambda_q = 2 cos(pi/q) which are closely related to the Hecke triangle
groups G_q, q=3,4,... . They have been introduced in the case q=3 by Hurwitz
and for even q by Nakada. These continued fractions are generated by interval
maps f_q respectively f_q^* which are conjugate to subshifts over infinite
alphabets. We generalize to arbitrary q a result of Hurwitz concerning the
G_q-- and f_q-equivalence of points on the real line. The natural extension of
the maps f_q and f_q^* can be used as a Poincare map for the geodesic flow on
the Hecke surfaces G_q\H and allows to construct the transfer operator for this
flow.
