Abstract: 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. 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.