Novel latching microfluidic valve structures are developed, characterized, and controlled independently using an on-chip pneumatic demultiplexer. These structures are based on pneumatic monolithic membrane valves and depend upon their normally-closed nature. Latching valves consisting of both three- and four-valve circuits are demonstrated. Vacuum or pressure pulses as short as 120 ms are adequate to hold these latching valves open or closed for several minutes. In addition, an on-chip demultiplexer is demonstrated that requires only n pneumatic inputs to control 2(n-1) independent latching valves. These structures can reduce the size, power consumption, and cost of microfluidic analysis devices by decreasing the number of off-chip controllers. Since these valve assemblies can form the standard logic gates familiar in electronic circuit design, they should be useful in developing complex pneumatic circuits.