  We shall investigate the possibility of formulation of varying speed of light
(VSL) in the framework of Palatini non-linear Ricci scalar and Ricci squared
theories. Different speeds of light including the causal structure constant,
electromagnetic, and gravitational wave speeds are discussed. We shall see that
two local frames are distinguishable and discuss about the velocity of light in
these two frames. We shall investigate which one of these local frames is
inertial.
