  In this work we explore the dynamics of the generalized hybrid
metric-Palatini theory of gravity in the weak-field, slow-motion regime. We
start by introducing the equivalent scalar-tensor representation of the theory,
which contains two scalar degrees of freedom, and perform a conformal
transformation to the Einstein frame. Linear perturbations of the metric in a
Minkowskian background are then studied for the metric and both scalar fields.
The effective Newton constant and the PPN parameter $\gamma$ of the theory are
extracted after transforming back to the (original) Jordan frame. Two
particular cases where the general method ceases to be applicable are
approached separately. A comparison of these results with observational
constraints is then used to impose bounds on the masses and coupling constants
of the scalar fields.
