A valved microfluidics device, microfluidics cell-culture device and system incorporating the devices are disclosed. The valved microfluidics device includes a substrate, a microchannel through which liquid can be moved from one station to another within the device, and a pneumatic microvalve adapted to be switched between open and closed states to control the flow of fluid through a microchannel. The microvalve is formed of three flexible membranes, one of which is responsive to pneumatic pressure applied to the valve and the other two of which deform to produce a more sealable channel cross-section. The cell culture device provides valving to allow controlled loading of cells into the individual well of the device, and exchange of cell-culture components in the wells.