The use of thermoacoustic principles to eliminate all moving parts from Stirling engines and refrigerators leads to devices with the inherently high efficiency of the Stirling cycle and the simplicity of no moving parts. We have demonstrated over 40% of the Carnot efficiency in such a device; higher efficiency appears to be possible. The gas dynamics resembles that of free-piston Stirling devices, but with gas inertia playing the role of piston masses. However, large time-averaged flows can be superimposed on the oscillating flows. Control of the time-averaged flows is essential to ensure that they do not reduce efficiency by convecting significant amounts of heat.