The paper concerns the analysis of a self-synchronization process of inertial vibrators in general motion. These types of systems are found e.g. in the case of vibratory conveyors, in which the synchronization plane of vibrators is perpendicular to the plane of vibration of the conveyor trough. The analysis is focused on two basic issues related to movement of the vibrator. The first issue concerns conditions for obtaining stable motion in a configuration ensuring generation of useful vibrations. The second one is determination of the value of the synchronizing moment. In order to obtain analytical dependencies as simply as possible, we considered a typical build conveyor and the suspension, whose mathematical description we can bring to a diagonal form. In the paper, we paid attention to the consequences of using suspensions with highly directional properties, e.g. metal-elastomer vibration isolators.