Two compliance structures for the use in liquid-based microfluidic systems have been realized with the aid of silicon micromachining. The basic principle is that these structures contain air bubbles that dampen the flow and pressure variations that may arise from a micropump. The compliance structures were specifically designed to work with the no moving parts valve (NMPV) pump [Proc. ASME Fluids Eng. Division, 1995, in press]. The structures were modeled and simulated. From the results of these simulations and the model, design rules for the compliance are formulated. Measurements on the compliance structures could only be performed for the steady state. These measurements were in very good agreement with the model. Working with two sets of pumps showed that pumps without the compliance structure needed an external compliance in order to get them to work, whereas the pumps with the on-chip compliance pumped right away.