  The upper bound on the value of the surface gravity, g_s, for neutron stars
with equations of state respecting v_sound <= c, is derived. This bound is
inversely proportional to the maximum allowable mass M_max, and it reads g_s <=
1.411 x 10^15 (M_sun/M_max) cm/s^2. It implies an absolute upper bound 7.4 x
10^14 cm/s^2 if one uses the 2sigma lower bound on the neutron mass measured
recently in 4U1700-37, 1.9 M_sun. A correlation between g_s and the compactness
parameter 2GM/Rc^2 for baryonic stars is analyzed. The properties of g_s of
strange quark stars and its upper bounds are discussed using the scaling
properties of the strange-star models.
