In previous studies,ve have considered several types of positive displacement rotary pumps and deeply analyzed the generation of the flow rate and the design limits. This has been done in order to evaluate the main performance indexes; one of which, the flow rate irregularity, is related to the possibility that the pump becomes a source of vibration and noise. A second index is the specific flow rate, related to the delivery capacity of the pump. In this paper, following our previous researches, we analyzed internal involute gear pumps and internal lobe pumps, that have similar operations bur different performances. The design parameters and the way to optimize the performances are proposed for both cases. Finally a comparison is made between the two types of pumps with optimum design parameters.