  We present new long-slit William Herschel Telescope spectroscopic
observations of the lens galaxy G1 associated with the double-imaged QSO
0957+561A,B. The obtained central stellar velocity dispersion, sigma_l = 310
+/- 20 km/s, is in reasonable agreement with other measurements of this
dynamical parameter. Using all updated measurements of the stellar velocity
dispersion in the internal region of the galaxy (at angular separations < 1".5)
and a simple isotropic model, we discuss the mass of a possible central massive
dark object. It is found that the data of Falco et al. (1997) suggest the
existence of an extremely massive object of (0.5-2.1) x 10E10/h M_\odot (80%
confidence level), whereas the inclusion of very recent data (Tonry & Franx
1998, and this paper) substantially changes the results: the compact central
mass must be $\le$ 6 x10E9/h M_\odot at the 90% confidence level. We note that,
taking into account all the available dynamical data, a compact nucleus with a
mass of 10E9/h M_\odot (best fit) cannot be ruled out.
